New results on dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information

This paper investigates the problem of delay‐dependent dynamic output feedback control for a class of discrete‐time Markovian jump linear systems (MJLSs). The systems under consideration are subject to time‐varying delay and defective mode information. The defective transition probabilities comprise of three types: exactly known, uncertain, and unknown. By employing a two‐term approximation for the time‐varying delay, the original MJLSs can be equivalently converted into a feedback interconnection form, which contains a forward subsystem with constant time‐delays and a feedback one with norm‐bounded uncertainties. Then, based on the scaled small‐gain theorem, the problem is therefore recast as an control problem in the face of uncertainties via an input–output framework. It is shown that the explicit expressions of the desired controller gains can be characterized in terms of strict linear matrix inequalities via some linearization techniques. Simulation studies are performed to illustrate the effectiveness and less conservatism of the proposed methods. Copyright © 2013 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.     

New delay‐dependent exponential stability for neutral Markovian jump systems with mixed delays and nonlinear perturbations

This paper deals with the problem of delay‐dependent exponential stability for neutral Markovian jump systems with mixed delays and nonlinear perturbations. Based on Lyapunov stability theory and linear matrix inequality method, some new exponential stability criteria are presented. The difference between this paper and other existing results is that the lower bounds of the neutral delay, the upper bounds of the neutral delay and discrete delay are considered, which will obtain some less conservative stability analysis results. Numerical examples are given to show that the proposed criteria improve the existing results.     

Stochastic faulty actuator‐based reliable control for a class of interval time‐varying delay systems with Markovian jumping parameters

The paper addresses the problem of a reliable control for interval time‐varying delay system with Markovian jumping parameters. A new practical actuator fault model, by assuming that the actuator fault obeys a certain probabilistic distribution, is considered. Delay‐dependent conditions for the solvability of these problems are obtained via new parameter‐dependent Lyapunov function. The closed‐loop systems are stochastically stable not only when all actuators are operational, but also in case of some actuator failures. Numerical examples are given to illustrate the effectiveness of the proposed design method. Copyright © 2010 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.     

Robust observer‐based control for uncertain discrete time‐delay systems with nonlinearities electric‐hydraulic system under Hölder condition

In this paper, the robustness and control problems of output dynamic observer‐based control for uncertain discrete time‐delay systems with nonlinearities under a class of Hölder condition are considered. The parameter uncertainties enter into all the system matrices, the time‐varying delay is unknown with given lower and upper bounds, and the nonlinearities are described by satisfying a class of α Hölder condition. The asymptotic stabilization for uncertain time‐delay nonlinear system will be guaranteed. Linear matrix inequality optimization approach is used to design the robust observer‐based output dynamic controls. The feedback control and observer gains are got from linear matrix inequality optimization feasible solution. Electric‐hydraulic system is described and used to illustrate the method.     

Reachable set estimation for neutral Markovian jump systems with mode‐dependent time‐varying delays

This study, under zero initial condition, aims to characterize the reachable set bound for a class of neutral Markovian jump systems (NMJSs) with interval time‐varying delays and bounded disturbances. To begin with, the time‐delays are considered to be mode‐dependent while delay mode and system mode are different. By utilizing free‐weighting matrix method and reciprocally convex combination technique, an ellipsoid‐like bound is characterized for the concerned NMJS with completely known transition probabilities. Based on the provided analytical framework, the case of same delay mode and system mode is also handled. Then, benefitting from a group of free‐connection weighting matrices, the reachable set estimation issue is tackled for the NMJS involving mode‐independent time‐varying delays and partially known transition probabilities. The theoretical analysis is confirmed by numerical simulations.     

Robust quantized feedback stabilization of linear systems based on sliding mode control

This paper investigates the robust quantized feedback stabilization problem for a class of single‐input linear uncertain systems on the basis of sliding mode control schemes. It is assumed that the system signals including the system state and control input are quantized before being transmitted through digital communication channels. A static adjustment policy of the quantization parameter for dynamic quantizers is developed. With the adjustment of the quantization parameter, a sliding mode control strategy is designed to ensure the reachability of the sliding manifold, and then, the system is induced into the stable sliding motion thereafter. Finally, an example is provided to illustrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Mean square stabilization of discrete‐time switching Markov jump linear systems

This paper considers a special class of hybrid system called switching Markov jump linear system. The system transition is governed by two rules. One is Markov chain and the other is a deterministic rule. Furthermore, the transition probability of the Markov chain is not only piecewise but also orchestrated by a deterministic switching rule. In this paper, the mean square stability of the systems is studied when the deterministic switching is subject to two different dwell time conditions, ie, having a lower bound and having both lower and high bounds. The main contributions of this paper are two relevant stability theorems for the systems under study. A numerical example is provided to demonstrate the theoretical results.     

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.     

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.     

Asynchronous control of time‐delayed switched systems with actuator saturation via anti‐windup design

This paper deals with the problem of asynchronous control for time‐delay switched systems under actuator saturation via anti‐windup design, where asynchronous switching means the switching of the controllers has a lag to the switching of subsystems. By constructing an appropriate piecewise Lyapunov‐Krasovskii function and using local sector conditions, sufficient conditions for solving the problem are derived in the form of linear matrix inequalities. Moreover, the domain of attraction is maximized. Finally, an application example is given to demonstrate the validity of the main results.     

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.     

ℋ︁∞ control of discrete‐time Markov jump systems with bounded transition probabilities

This paper deals with the class of discrete‐time linear systems with random abrupt changes and unknown transition probabilities but varying between known bounds for each mode. The ℋ︁_∞ control problem of this class of systems is revisited and new sufficient conditions are developed in the linear matrix inequality (LMI) setting to design the state‐feedback controller that stochastically stabilizes the system under consideration and at the same time guarantees the disturbance rejection with a desired level γ . Sufficient conditions for existence of the state‐feedback controller are developed. It is shown that the addressed problem can be solved if the corresponding developed LMIs are feasible. Numerical examples are employed to show the usefulness of the proposed results. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal integral sliding mode control for a class of uncertain discrete‐time systems

This paper considers the problem of sliding mode control for a class of uncertain discrete‐time systems. Firstly, an optimal control law for the nominal system is derived to satisfy linear quadratic performance index. And then, an optimal integral sliding surface is designed to ensure the robustness for sliding dynamics. By combining with the discrete reaching law, the existence condition of the sliding mode is proved, and the bandwidth of the quasi‐sliding mode is given. It is shown that the present method utilizes a lower control gain to attain stronger robustness and eliminate the chattering. Finally, illustrative simulation results are provided. Copyright © 2013 John Wiley & Sons, Ltd.     

Mixed H2/H∞ robust output feedback sliding mode control

This paper presents an output feedback sliding mode control scheme for uncertain dynamical systems. The design problem is solved in two steps, involving first a state feedback and then an output feedback problem. First, using the null space dynamics, the sliding surface for the unmatched uncertainty is designed. Then, by tuning the sliding surface, a robust controller is constructed for the whole uncertainty; this problem takes the form of static‐output feedback. Based on this, a dynamic output feedback controller for the system augmented with the sliding surface is designed. The synthesis involves the solution of an Linear Matrix Inequality (LMI) and Bilinear Matrix Inequality (BMI) problem; the BMI problem is solved iteratively. The proposed approach is illustrated by applying it to a well‐known robust benchmark problem and also experimentally on a spring mass system with variable stiffness. Simulation and experimental results show that the proposed method outperforms previous approaches in terms of robust performance. Copyright © 2011 John Wiley & Sons, Ltd.     

Mixed and passive filtering for a class of singular systems with interval time‐varying delays

This paper deals with the problem of mixed and passive filtering for a class of singular systems with interval time‐varying delays. First, by combining the Wirtinger‐based integral inequality with the reciprocally convex inequality, sufficient delay‐range‐dependent conditions are obtained in terms of strict linear matrix inequalities to ensure that the considered singular system is admissible with a mixed and passivity performance level. Then, based on a matrix transformation technique and employing several free scalars, more flexible strict linear matrix inequality–based conditions are proposed to get the desired filter. Finally, 2 numerical examples are given to show less conservatism and the effectiveness of the results.     

A note on the robust control of Markov jump linear uncertain systems

This note addresses a robust control problem of continuous‐time jump linear Markovian systems subject to norm‐bounded parametric uncertainties. The problem is expressed in terms of a H_∞ control problem as in the purely deterministic case. The present formulation is simpler and it contains previous results in the literature as particular cases. Robust state feedback controllers are parameterized by means of a set of linear matrix inequalities. The result is illustrated by solving some examples numerically. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust reliable guaranteed cost control for uncertain T‐S fuzzy neutral systems with interval time‐varying delay and linear fractional perturbations

The robust reliable guaranteed cost control for Takagi–Sugeno fuzzy systems with interval time‐varying delay is considered in this paper. Some free weighting matrices and non‐negative terms are provided to improve the conservativeness of our main results. An LMI optimization approach is applied to solve the problems of robust reliable guaranteed cost control and minimization of cost function. Copyright © 2014 John Wiley & Sons, Ltd.