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.     

Mixed H2/H∞ control for a class of nonlinear discrete‐time networked control systems with random delays and stochastic packet dropouts

The paper studies the problem of mixed H₂/H_∞ control for a class of nonlinear discrete‐time networked control systems. By using the indicator function method, random network‐induced delays and stochastic packet dropouts are taken into account in a unified framework in the designed mixed H₂/H_∞ controller. In the presences of random transmission delays, stochastic packet dropouts and all admissible disturbances, the resulting closed‐loop system is stochastically stable in mean square and attains the prescribed H₂ and H_∞ performances. The designed mixed H₂/H_∞ controller can be obtained by solving a set of feasible linear matrix inequalities. Finally, a numerical example is provided to show the usefulness and effectiveness of the developed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust H∞ control for uncertain linear neutral delay systems

This paper deals with the problem of robust H_∞ control for uncertain linear neutral delay systems. The parameter uncertainty under consideration is assumed to be norm‐bounded time‐invariant and appears in all the matrices of the state‐space model. The problem we address is the design of memoryless state feedback controllers such that the closed‐loop system is asymptotically stable and the H_∞ norm of the closed‐loop transfer function from disturbance to the controlled output is strictly less than a prescribed positive scalar for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the above problem is proposed. When this matrix inequality is feasible, an explicit expression for the desired state feedback controller is given. Furthermore, a numerical example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2002 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.     

H∞ control for sampled‐data linear systems with two Markov processes

This paper is concerned with the design problem of H_∞ digital switching control for linear continuous systems with Markovian jumping parameters. The controller is digital and monitored by the jumping parameters of the plant. The closed‐loop system is a hybrid one defined on a hybrid time space (composed of a continuous‐time and a discrete‐time) and a sample space. The sample space is specified by two separable continuous‐time discrete‐state Markov processes, one appearing in the open‐loop system, and the other appearing in control action, which is different with the traditional Markovian jumping process. Our attention is focused on designing digital output feedback controllers for the system with two Markovian jumping processes such that both stochastic stability and a prescribed H_∞ performance are achieved. The problem of robust H_∞ control for systems with parameters uncertainties is also studied. It is shown that the sampled‐data control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of intercoupled matrix inequalities. Two numerical examples are given to show the design procedures. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust resilient H ∞ control for stochastic systems with Markovian jump parameters under partially known transition probabilities

In this paper, the robust resilient H _∞ control problem for a class of stochastic systems with partially known transition probabilities is investigated. The system under consideration finds extensive applications because of the uncertainties involved in the system matrices and the general assumption upon the transition probabilities. Attention is focused upon the design of a robust resilient H _∞ state feedback controller, which guarantees the stochastic stability of the closed‐loop system and a prescribed H _∞ disturbance attenuation level for all admissible uncertainties. Sufficient criteria ensuring the stochastic stability and stabilization of the underlying systems are presented via LMIs formulation. A numerical example is provided to demonstrate the effectiveness of all the results. Copyright © 2013 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.     

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 H∞ output feedback design for networked control systems with partially known delay probabilities

This article develops a predictive robust H_∞ static output feedback control approach for networked control systems where random network-induced delays in both forward and feedback communication channels are modeled as two mutually uncorrelated Markov chains. By making use of the system augmentation method, the closed-loop system is formulated as a singular Markovian jump system with two modes, wherein the transition probability matrices of the underlying Markov chains are considered to be partially accessible. Necessary and sufficient conditions for the stochastic admissibility and robust H_∞ performance of the closed-loop system are given under the assumption of partially known transition probability matrices. A linear matrix inequality condition is proposed to determine the two-mode-dependent static output feedback controller gains to compensate for the random network-induced delays efficiently and provide the desired control performance. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.     

H∞ control of switched linear discrete‐time systems with polytopic uncertainties

In this paper, the problem of designing H_∞ state‐feedback controllers for switched linear discrete‐time systems with polytopic uncertainties is investigated. Two approaches on designing robust and parameter‐dependent H_∞ controllers are proposed and the existence conditions of the desired controllers are derived and formulated in terms of a set of linear matrix inequalities. By solving the corresponding convex optimization problem, the desired controllers are obtained, respectively, and different optimal H_∞ noise‐attenuation level bounds of corresponding closed‐loop systems are given as well. The designed controllers have their own advantages and disadvantages regarding the conservatism and realization complexity. An illustrative example emerging in networked control systems (NCS) and numerical simulations are presented to show the applicability and effectiveness of the obtained theoretic results. Copyright © 2006 John Wiley & Sons, Ltd.     

Further results on H ∞ control for discrete‐time uncertain singular systems with interval time‐varying delays in state and input

This paper investigates the state feedback robust H _∞ control problem of a class of discrete‐time singular systems with norm‐bounded uncertainties and interval time‐varying delays in state and input. A new bounded real lemma for discrete‐time singular systems with a pair of time‐varying interval state delays is first investigated. Mathematical comparisons of the new bounded real lemma and two existing ones are presented. Then, on the basis of the bounded real lemma proposed here, a sufficient condition in the form of nonlinear matrix inequality, such that the considered state feedback robust H _∞ control problem is solvable, is given. In order to solve the nonlinear matrix inequality, a cone complementarity linearization algorithm is offered. Several numerical examples are presented to show the applicability of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust H∞ output feedback control for Markovian jump systems with actuator saturation

This paper concerns the output feedback control problem for a class of uncertain continuous‐time Markovian jump systems with actuator saturation. The controller is nonlinear in nature and will be first parameterized in the quasi‐linear parameter varying form. Conditions under which the closed‐loop system is stochastically stable with γ disturbance attenuation are then derived in terms of an LMI approach. The problem of designing an output feedback controller such that the estimate of the domain of attraction is enlarged is then formulated and solved as an optimization problem with LMI constraints. The case where the transition rate matrix of the Markov process is unknown is considered, and the robust H_∞ output feedback controller is then derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed results. Copyright © 2011 John Wiley & Sons, Ltd.     

Controlling the discrete-time conic-type nonlinear system by a time-delayed robust controller

This paper investigates the robust H_∞ controller design problem for a class of discrete-time conic-type nonlinear systems with time delays and uncertainties. We aim to design a time-delayed feedback control law such that the closed-loop conic-type nonlinear system is asymptotically stable and satisfies the given H_∞ performance index from the controlled output to the external disturbance. By selecting a proper Lyapunov function, sufficient conditions related to the H_∞ stabilization are formulated in the form of linear matrix inequalities. Finally, a simulation example is employed to demonstrate the effectiveness of the proposed methods.     

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.     

Event‐triggered and guaranteed cost finite‐time H∞ control for uncertain switched linear systems

This paper is concerned with the event‐triggered and guaranteed cost finite‐time H_∞ control problem for uncertain switched linear systems with exogenous disturbance. Instead of one common strategy, multiple event‐triggering strategies are first proposed, ie, each subsystem possesses its own corresponding event‐triggering substrategy. Then, by utilizing the multiple Lyapunov functions and average dwell‐time method, sufficient conditions for the finite‐time boundedness with an H_∞ performance level of the resulting event‐triggered switched closed‐loop system are derived. Meanwhile, a certain upper bound of the guaranteed cost function with respect to the system uncertainties is obtained. Subsequently, a set of sufficient conditions in terms of linear matrix inequalities is given for solving the event‐triggered and guaranteed cost finite‐time H_∞ state feedback controllers. Furthermore, the Zeno sampling behavior is excluded by presenting a positive lower bound estimation on the interexecution intervals. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed approach.     

The improved H∞ controller design for nonlinear networked control systems with random communication delays

This paper is concerned with the observer‐based H_∞ controller design problem for nonlinear networked control systems with random communication delays. Firstly, the dynamic observer‐based control scheme is modelled, where the control input of the observer is different from the control input of the plant. Then, a less conservative delay‐dependent H_∞ stabilization criterion is derived by using an improved Lyapunov function. And the proof of stabilization criterion is completed in terms of four cases when the time delays in two communication channels are constant or time‐varying, respectively. The derived stabilization criterion is formulated in the form of a non‐convex matrix inequality, which can be solved by an optimal cone complementary linearization iteration algorithm to obtain the minimum disturbance attenuation level. Finally, several numerical examples and an illustrative example are provided to clarify the effectiveness and merits of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust H∞ control for stochastic time‐delayed Markovian switching systems under partly known transition rates and actuator saturation via anti‐windup design

The paper deals with the problem of robust H_∞ control for stochastic time‐delayed Markovian switching systems under partly known transition rates and actuator saturation via anti‐windup design. The problem we address is the design of anti‐windup compensators, which guarantee that the resulting closed‐loop system is robustly stochastically stable with H_∞ performance. By employing local sector conditions and an appropriate Lyapunov–Krasovskii function, sufficient conditions for solving the problem are derived in the form of linear matrix inequalities. Finally, numerical examples are given to demonstrate the validity of the main results. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust sliding mode design for uncertain stochastic systems based on H∞ control method

In this paper, the design problem of sliding mode control (SMC) is addressed for uncertain stochastic systems modeled by Itô differential equations. There exist the parameter uncertainties in both the state and input matrices, as well as the unmatched external disturbance. The key feature of this work is the integration of SMC method with H_∞ technique such that the robust stochastic stability with a prescribed disturbance attenuation level γ can be achieved. A sufficient condition for the existence of the desired sliding mode controller is obtained via linear matrix inequalities. The reachability of the specified sliding surface is proven. Finally, a numerical simulation example is presented to illustrate the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

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.