Improved approach for passive stability of discrete‐time Markovian jump linear systems via mode‐dependent time‐delayed controllers

In this paper, we investigate the problem of passive stability for discrete‐time Markovian jump linear systems via mode‐dependent time‐delayed controllers by employing an improved free‐weighting matrix approach. A Markov process as discrete‐time, discrete‐state Markov process is considered. First, a new result of mode‐dependent stability analysis is first established for error systems without ignoring any terms in the derivative of Lyapunov–Krasovskii function by considering the relationship between the time‐varying delay and its upper bound. Then, the delay‐dependent passivity criterion is provided and a mode‐dependent time‐delayed controller is designed in terms of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

A µ‐dependent approach to H∞ control of uncertain switched linear systems with average dwell time

This paper concerns H_∞ control problem for a class of discrete‐time uncertain switched linear systems with average dwell time. The stability result for general discrete‐time switched systems is first explored, and a µ‐dependent approach is then introduced for the considered systems to the H_∞ controller solution. A mode‐dependent state‐feedback controller is designed such that the resulting closed‐loop system is robust exponentially stable and has a prescribed exponential H_∞ performance index. The µ‐dependent existence conditions of desired controller and admissible switching signals are derived and formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the developed theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

Stochastic control of networked control systems with packet dropout and time‐varying delay

This paper studies the stochastic stabilization problem for discrete‐time networked control systems with time delay and packet dropout. The message losses and time delay from the sensor to the controller and from the controller to the actuator are considered simultaneously. A two‐state Markov chain is used to model the correlated packet dropout process. By introducing free weighting matrices, the sufficient condition on the stochastic stability of such networked control system is obtained. An improved criterion is found by introducing the delay fractioning method and a new Lyapunov–Krasovskii functional. On the basis of the stability condition, the mode‐dependent controller is given in terms of linear matrix inequalities. A simulation example is given to show the proposed results. Copyright © 2012 John Wiley & Sons, Ltd.     

Delay‐dependent H∞ control for singular Markovian jump systems with time delay

The problem of delay‐dependent H_∞ control is considered for singular Markovian jump systems with time delay. The aim of the problem is to design a state feedback controller, which guarantees that the resultant closed‐loop system is not only regular, impulse free and stochastically stable, but also satisfies a prescribed H_∞ performance level for all delays no larger than a given upper bound in terms of linear matrix inequality (LMI) approach. A strict LMI condition is developed to guarantee the existence of the desired state feedback controller. An explicit expression for the desired controller is also given. Numerical examples show the effectiveness of the proposed methods. Copyright © 2008 John Wiley & Sons, Ltd.     

Fixed‐structure controller design for polytopic systems via LMIs

In this paper, a new approach for fixed‐structure H₂ controller design in terms of solutions to a set of linear matrix inequalities are given. Both discrete‐time and continuous‐time SISO time‐invariant systems are considered. Then the results are extended to systems with polytopic uncertainty. The presented methods are based on an inner convex approximation of the non‐convex set of fixed‐structure H₂ controllers. The designed procedures are initialized either with a stable polynomial or with a stabilizing controller. An iterative procedure for robust controller design is given that converges to a suboptimal solution. The monotonic decreasing of the upper bound on the H₂ norm is established theoretically for both nominal and robust controller design. Copyright © 2014 John Wiley & Sons, Ltd.     

Delay‐dependent guaranteed cost gain‐scheduling control of LPV state‐delayed systems

Delay‐dependent gain‐scheduling controller design problem is addressed for the linear parameter‐varying state‐delayed systems with time‐varying delays. By choosing a Lyapunov–Krakovskii functional, delay‐dependent conditions for the existence of guaranteed cost gain‐scheduling controller are obtained. Besides, an algorithm is also presented to solve resultant nonconvex matrix inequalities in terms of linear matrix inequalities. Finally, three numerical examples with simulations are illustrated in order to demonstrate the validity of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Mode feedback control strategy for continuous‐time Markovian jump linear systems with controllable mode transition rate matrix

This paper investigates mode feedback control strategy for continuous‐time Markovian jump linear systems with controllable mode transition rate matrix (MTRM). Based on the fact that system stability as well as its performance is dependent on MTRM, a mode feedback controller is proposed to perform control on MTRM such that system stability is achieved. Meanwhile, this strategy can help to improve system performance since it can adjust the occurrence probability of each subsystem. Firstly, taking into account that MTRM will totally determine system stability in absence of state feedback controller, the existence and restrictions on mode feedback controller are discussed where two cases are included. Then, based on a quadratic stabilization cost function that is a combination of state cost and control cost, a feasible solution of mode feedback control strategy is then obtained with its detailed algorithm given. Simulation results including comparisons with current state feedback mechanism are provided to illustrate the effectiveness of the proposed strategy.     

Delay‐dependent feedforward control of time‐delay systems with parametric uncertainties via dynamic IQCs

This paper studies the design problem of a robust delay‐dependent H _∞ feedforward controller design for a class of linear uncertain time‐delay system having state and control delays when the system is subject to ‐type disturbances. The proposed controller scheme involves two main controllers, which are static state‐feedback and dynamic feedforward controllers. The state‐feedback controller is used for stabilizing the delay and uncertainty‐free system, whereas the feedforward controller performs disturbance attenuation. Dynamic type integral quadratic constraints (IQCs), which consist of frequency‐dependent multipliers, have been introduced to represent the delays and parametric uncertainties in the system where the degree of the multiplier used in IQC representation is in an adjustable nature. This scheme allows the designer to obtain less conservative controllers with increasing precision. Sufficient delay‐dependent criteria in terms of linear matrix inequalities are obtained such that the uncertain linear time‐delay system is guaranteed to be globally, uniformly, asymptotically stable with a minimum disturbance attenuation level. Several numerical examples together with the simulation studies provided at the end illustrate the usefulness of the proposed design. Copyright © 2012 John Wiley & Sons, Ltd.     

H∞ state‐feedback controller design for continuous‐time nonhomogeneous Markov jump systems

This paper studies the problem of H_∞ state‐feedback controller design for continuous‐time nonhomogeneous Markov jump systems. The time‐varying transition rate matrix in continuous‐time domain is considered to lie in a convex bounded domain of polytopic type. By constructing a parameter‐dependent Lyapunov function and fully considering the information about the rate of change of time‐varying parameters, a new sufficient condition on the existence of an H_∞ state‐feedback controller is provided in the form of a parameter‐dependent matrix inequality. Moreover, based on the structure characteristics of Lyapunov matrix and transition matrix, the parameter‐dependent matrix inequality is converted into a finite set of linear matrix inequalities, which can be readily solved. Two numerical examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal guaranteed cost synchronization of coupled neural networks with Markovian jump and mode‐dependent mixed time‐delay

This paper is concerned with the optimal guaranteed cost synchronization problem for a class of coupled neural networks with Markovian jump parameters and mode‐dependent mixed time‐delay. The coupled neural networks contained N‐identical delayed neural nodes and M switch modes from one mode to another according to a Markovian chaining with known transition probability. All the coupled networks' parameters covering the coupled matrix and discrete and distributed time‐delay also depend on the Markovian jump mode. The associated optimal guaranteed cost function is a quadratic function; the activation function is supposed to satisfy sector‐bounded condition. By employing a new Lyapunov–Krasovskii functional and some analytic skills, the sufficiency conditions of guaranteed cost synchronization are derived to ensure that coupling neural network is asymptotically synchronized for related cost function in mean square. The exported sufficient condition is closely contacted with the distributed time‐delay, the mode transition probability, the discrete‐time delay, and the coupled structure of networks. The achieved conditions are given in the light of LMI that can be usefully solved by using the semi‐definite program scheme. Moreover, an LMI‐based approach to export the guaranteed cost synchronization controller is formulated to minimize the optimal guaranteed cost for closed‐loop dynamical networks. Numerical simulations are developed to further display the efficiency of the achieved theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Delay‐dependent output feedback L1 control for positive Markovian jump systems with mode‐dependent time‐varying delays and partly known transition rates

The paper deals with the problem of delay‐dependent output feedback L₁ control for positive Markovian jump systems with mode‐dependent time‐varying delays and partly known transition rates. First, by constructing an appropriate co‐positive type Lyapunov function, sufficient conditions for stochastic stability and L₁‐gain performance of the open‐loop system are developed. Then, an effective method is proposed to construct the output feedback controller. These sufficient criteria are derived in the form of linear programming. A key point of this paper is to extend the special requirement of completely known transition rates to more general form that covers completely known and completely unknown transition rates as two special cases. Finally, a numerical example is given to illustrate the validity of the main results. Copyright © 2016 John Wiley & Sons, Ltd.     

Delay‐dependent robust passive control for a class of nonlinear systems with time‐varying delays

In this paper, the problem of robust passive control for a class of nonlinear systems with time‐varying delays is considered. The uncertainties investigated in this paper are norm bounded and time varying, and they enter all system matrices. Based on the Lyapunov–Krasovskii functionals approach, a new robust passive control criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of time delay. We also design a state feedback controller that guarantees a robust asymptotically stable and strictly passive closed‐loop system for all admissible uncertainties. Finally, two numerical examples are given to illustrate the effectiveness of the developed techniques. Copyright © 2007 John Wiley & Sons, Ltd.     

Design of sliding mode control for neutral delay systems with perturbation in control channels

This paper considers the problem of sliding mode control for a class of uncertain neutral delay systems. There are uncertainties not only in the state matrices, but also in the control matrix that results from perturbation in the control channels. By means of a sliding surface dependent on both the current states and delayed states, a sliding mode controller is designed such that the asymptotic stability of closed‐loop systems can be ensured. The design of both the sliding surface and the sliding mode controller can be obtained via convex optimization. It is shown that the state trajectories are driven onto the specified sliding surface in finite time and remain there for subsequent time. Finally, a numerical simulation example is provided. Copyright © 2011 John Wiley & Sons, Ltd.     

H∞ output tracking control over networked control systems with Markovian jumping parameters

The problem of H_∞ output tracking control over networked control systems (NCSs) with communication limits and environmental disturbances is studied in this paper. A wide range of time‐varying stochastic problem arising in networked tracking control system is reduced to a standard convex optimization problem involving linear matrix inequalities (LMIs). The closed‐loop hybrid NCS is modeled as a Markov jump linear system in which random time delays and packet dropouts are described as two stochastic Markov chains. Gridding approach is introduced to guarantee the finite value of the sequences of transmission delays from sensor to actuator. Sufficient conditions for the stochastic stabilization of the hybrid NCS tracking system are derived by the LMI‐based approach through the computation of the optimal H_∞ performance. The mode‐dependent robust H_∞ output tracking controller is obtained by the optimal iteration method. Numerical examples are given to demonstrate the effectiveness of the proposed robust output tracking controller for NCS. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust H∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

This paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H_∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed.     

Singular linear systems with delay: ℋ︁∞ stabilization

This paper deals with the class of continuous‐time singular linear systems with time‐delay in the state vector. The stabilization problem of this class of systems using a state feedback controller is tackled. New delay‐dependent sufficient conditions on ??_∞ stabilization are developed. A design algorithm for a memoryless state feedback controller which guarantees that the closed‐loop dynamics will be regular, impulse‐free and stable with γ‐disturbance rejection is proposed. It is shown that the addressed problem can be solved if the corresponding developed linear matrix inequalities (LMIs) with some constraints are feasible. A numerical example is employed to show the usefulness of the proposed results. Copyright © 2007 John Wiley & Sons, Ltd.     

Delay‐dependent robust H ∞ control for uncertain singular time‐delay system with Markovian jumping parameters

The problem of robust H _∞ control for a class of uncertain singular time‐delay systems with Markovian jumping parameters is addressed in this paper. The considered Markovian jump singular systems involve constant time delay and norm‐bounded uncertainties. On the basis of LMI approach, a delay‐dependent condition is proposed, which ensures the nominal Markovian jump singular system to be regular, impulse‐free and stochastically stable. From the delay‐dependent condition, a sufficient condition leading to the existence of a state feedback controller that guarantees the robust admissibility and the H _∞ performance is also given. A numerical example is given to demonstrate the applicability of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust reliable control for discrete‐time‐delay systems with stochastic nonlinearities and multiplicative noises

This paper is concerned with the reliable control problem against actuator failures for a class of uncertain discrete‐time stochastic nonlinear time‐delay systems. The failures of actuators are quantified by a variable varying in a given interval. The stochastic nonlinearities described by statistical means cover several well‐studied nonlinear functions as special cases. The time‐varying delay is unknown with given lower and upper bounds. The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. Attention is focused on the analysis and design of a stable controller such that, for all possible actuator failures, stochastic nonlinearities and disturbances, time delays and admissible parameter uncertainties, the closed‐loop system is exponentially mean‐square stable. A linear matrix inequality approach is developed to solve the addressed problem. A numerical example is given to demonstrate the effectiveness of the proposed design approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust static and fixed‐order dynamic output feedback control of discrete‐time parametric uncertain Luré systems: Sequential SDP relaxation approaches

Design methods are proposed for static and fixed‐order dynamic output feedback controllers for discrete‐time Luré systems with sector‐bounded nonlinearities in the presence of parametric uncertainties described by polytopes. The derived design conditions are represented in terms of bilinear matrix inequalities, which are nonconvex. By using convex relaxation methods, controller design equations are derived for systems with multiple states, outputs, and nonlinearities in terms of linear matrix inequalities (LMIs) and iterative LMIs, which are associated with semidefinite programs. The proposed design methods are developed from stability conditions using parameter‐dependent Lyapunov functions, and existing iterative numerical methods are adapted to solve certain classes of nonconvex optimization problems for controller design. Several numerical examples are provided to illustrate and verify the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Observer‐based H∞ control for uncertain singular time‐delay systems with actuator saturation

In this paper, the observer‐based H_∞ control problem for uncertain singular time‐delay systems with actuator saturation is concerned. First, a delay‐dependent linear matrix inequality (LMI) condition is obtained which, guarantees that the uncertain singular time‐delay systems with actuator saturation are regular, impulse free, and asymptotically stable with H_∞ performance condition. Then, with this condition, the estimation of stability region and the design method of observer‐based H_∞ controller are given by solving LMIs and convex optimization problem. Finally, some numerical examples are provided to demonstrate the merit of the obtained results. Copyright © 2015 John Wiley & Sons, Ltd.