State feedback control for uncertain switched systems with interval time‐varying delay

Stability criteria and hybrid controllers' design problems for a class of uncertain switched systems with interval time‐varying delay are considered in this paper. Based on the average dwell time method, by choosing a new appropriate Lyapunov‐Krasovskii functional which fully utilizes the information of both the lower and upper bounds of the interval time‐varying delay, new delay‐range‐dependent stability criteria and stabilization conditions are first derived in terms of linear matrix inequalities. Moreover, in order to obtain much less conservative results, a tighter bounding for some terms is estimated and no redundant matrix variable is introduced. Finally, two numerical examples are given to demonstrate the applicability and the effectiveness of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

H∞ filtering for singular systems with time‐varying delay

This paper is concerned with the delay‐dependent H_∞ filtering problem for singular systems with time‐varying delay in a range. In terms of linear matrix inequality approach, the delay‐range‐dependent bounded real lemmas are proposed, which guarantee the considered system to be regular, impulse free and exponentially stable while satisfying a prescribed H_∞ performance level. The sufficient conditions are proposed for the existence of linear H_∞ filter. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Stability and stabilization of discrete‐time singular Markov jump systems with time‐varying delay

The stochastic stability and stochastic stabilization of time‐varying delay discrete‐time singular Markov jump systems are discussed. For full and partial knowledge of transition probabilities cases, delay‐dependent linear matrix inequalities (LMIs) conditions for the systems to be regular, causal and stochastically stable are given. Sufficient conditions are proposed for the existence of state feedback controller in terms of LMIs. Finally, two numerical examples to illustrate the effectiveness of the method are given. Copyright © 2009 John Wiley & Sons, Ltd.     

Delay‐range‐dependent robust H∞ filtering for uncertain systems with interval time‐varying delays

This paper is concerned with the problem of delay‐range‐dependent robust H_∞ filtering for systems with time‐varying delays in a range. The aim of this problem is to design a filter such that, for all admissible uncertainties, the filtering error system is robustly asymptotically stable with a prescribed H_∞ level. The desired filter can be constructed by solving a set of linear matrix inequalities (LMIs). An illustrative numerical example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust stability of nonlinear time‐delay systems with interval time‐varying delay

This paper deals with the problem of obtaining delay‐dependent stability conditions and L₂‐gain analysis for a class of nonlinear time‐delay systems with norm‐bounded and possibly time‐varying uncertainties. No restrictions on the derivative of the time‐varying delay are imposed, though lower and upper bounds of the delay interval are assumed to be known. A Lyapunov–Krasovskii functional approach is proposed to derive novel delay‐dependent stability conditions which are expressed in terms of linear matrix inequalities (LMIs). To reduce conservatism, the work exploits the idea of splitting the delay interval in multiple regions, so that specific conditions can be imposed to a unique functional in the different regions. This improves the computed bounds for certain delay‐dependent integral terms, providing less conservative LMI conditions. Examples are provided to demonstrate the reduced conservatism with respect to the available results in the literature. Copyright © 2010 John Wiley & Sons, Ltd.     

Stabilization of nonlinear uncertain systems with stochastic actuator failures and time‐varying delay

In this paper, we investigate the adaptive state‐feedback stabilization problem for a class of nonlinear systems subject to parametric uncertainties, time‐varying delay, and Markovian jumping actuator failures. First, some fundamental results, including the infinitesimal generator and conditions for the existence and uniqueness of the solution, are established for nonlinear systems w.r.t. Markovian vector and time‐varying delay. Subsequently, corresponding stability criterion is generalized to the considered systems. By employing the backstepping method and the tuning function technique, a systematic adaptive fault‐tolerant control scheme is proposed, which guarantees the boundedness in probability of all the closed‐loop signals. It is noted that no fault detection and diagnostic block are needed, and the control law can be adapted automatically by taking account of the innovative state information. The efficiency of the designed controller is demonstrated by an illustrative example. Copyright © 2015 John Wiley & Sons, Ltd.     

Delay‐distribution‐dependent robust stability of uncertain systems with time‐varying delay

By employing the information of the probability distribution of the time delay, this paper investigates the problem of robust stability for uncertain systems with time‐varying delay satisfying some probabilistic properties. Different from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delay is random and its probability distribution is known a priori. In terms of the probability distribution of the delay, a new type of system model with stochastic parameter matrices is proposed. Based on the new system model, sufficient conditions for the exponential mean square stability of the original system are derived by using the Lyapunov functional method and the linear matrix inequality (LMI) technique. The derived criteria, which are expressed in terms of a set of LMIs, are delay‐distribution‐dependent, that is, the solvability of the criteria depends on not only the variation range of the delay but also the probability distribution of it. Finally, three numerical examples are given to illustrate the feasibility and effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

State feedback controller design of networked control systems with interval time‐varying delay and nonlinearity

This paper proposes a method for robust state feedback controller design of networked control systems with interval time‐varying delay and nonlinearity. The key steps in the method are to construct an improved interval‐delay‐dependent Lyapunov functional and to introduce an extended Jessen's inequality. Neither free weighting nor model transformation is employed in the derivation of system stability criteria. It is shown that the maximum allowable bound on the nonlinearity could be computed through solving a constrained convex optimization problem; and the maximum allowable delay bound and the feedback gain of a memoryless controller could be derived by solving a set of linear matrix inequalities. Numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Improved robust stability criteria for uncertain systems with time‐varying delay

This paper is concerned with the delay‐dependent stability and robust stability for uncertain systems with time‐varying delay. Through constructing an appropriate type of Lyapunov‐Krasovskii functional and proving its positive definiteness, using slack matrices and a convex combination condition, the delay‐dependent stability criteria, which are less conservative, are derived in terms of linear matrix inequalities. Numerical examples are also given to illustrate the improvement on the conservatism of the delay bound over some existing results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay‐range‐dependent robust stability and stabilization for uncertain systems with time‐varying delay

This paper concerns delay‐range‐dependent robust stability and stabilization for time‐delay system with linear fractional form uncertainty. The time delay is assumed to be a time‐varying continuous function belonging to a given range. On the basis of a novel Lyapunov–Krasovskii functional, which includes the information of the range, delay‐range‐dependent stability criteria are established in terms of linear matrix inequality. It is shown that the new criteria can provide less conservative results than some existing ones. Moreover, the stability criteria are also used to design the stabilizing state‐feedback controllers. Numerical examples are given to demonstrate the applicability of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Delay‐dependent robust control for singular discrete‐time Markovian jump systems with time‐varying delay

The problem of delay‐dependent robust stabilization for uncertain singular discrete‐time systems with Markovian jumping parameters and time‐varying delay is investigated. In terms of free‐weighting‐matrix approach and linear matrix inequalities, a delay‐dependent condition is presented to ensure a singular discrete‐time system to be regular, causal and stochastically stable based on which the stability analysis and robust stabilization problem are studied. An explicit expression for the desired state‐feedback controller is also given. Some numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Tracking control for switched linear systems with time‐delay: a state‐dependent switching method

Tracking control for switched linear systems with time‐delay is investigated in this paper. Based on the state‐dependent switching method, sufficient conditions for the solvability of the tracking control problem are given. We use single Lyapunov function technique and a typical hysteresis switching law to design a tracking control law such that the H_∞ model reference tracking performance is satisfied. The controller design problem can be solved efficiently by using linear matrices inequalities. Since convex combination techniques are used to derive the delay independent criteria, some subsystems are allowed to be unstable. It is highly desirable that a non‐switched time‐delay system can not earn such property. Simulation example shows the feasibility and validity of the switching control law. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust adaptive fault‐tolerant tracking control for uncertain linear systems with time‐varying performance bounds

In this paper, the problem of robust adaptive fault‐tolerant tracking control with time‐varying performance bounds is investigated for a class of linear systems subject to parameter uncertainties, external disturbances and actuator failures. In order to ensure the norm of the tracking error less than the user‐defined time‐varying performance bounds, we propose a new control strategy which is predicated on the generalized restricted potential function. Compared with the existing result, a novel method which provides two design freedoms is developed to reduce the tracking error. According to the online estimation information provided by adaptive mechanism, a fault‐tolerant tracking control method guaranteeing time‐varying performance bounds is developed for robust tracking of reference model. It is shown that the closed‐loop signals are bounded and the tracking error within an a priori given, time‐varying performance bounds. A simulation result is provided to demonstrate the efficacy of the proposed fault‐tolerant tracking control method.     

A delay‐dependent bounded real lemma for singular LPV systems with time‐variant delay

This paper is concerned with establishing a delay‐dependent bounded real lemma (BRL) for singular linear parameter‐varying (LPV) systems with time‐variant delay. In terms of linear matrix inequality, a delay‐dependent BRL is presented to ensure singular time‐delay LPV systems to be admissible and satisfy a prescribed H_∞ performance level. The BRL is obtained based on the construction of a parameter‐dependent Lyapunov–Krasovskii functional. The effectiveness of the proposed approach is shown by several numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Finite‐time stabilization for a class of nonlinear systems with time‐varying delay

This paper investigates the finite‐time stabilization problem for a class of nonlinear systems with time‐varying delay. Under suitable assumptions, a new state feedback control law is designed by using the adding a power integrator technique. By constructing an appropriate Lyapunov‐Krasovskii functional, it is shown that the corresponding closed‐loop system is finite‐time stable. Two simulation examples are given to verify the effectiveness of the proposed scheme.     

New results of stability analysis for systems with time‐varying delay

This paper studies the problem of stability analysis for continuous‐time systems with time‐varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration, and new delay‐dependent sufficient stability criteria are obtained in terms of linear matrix inequalities. The merits of the proposed results lie in their less conservatism, which are realized by choosing different Lyapunov matrices in the decomposed integral intervals and estimating the upper bound of some cross term more exactly. Numerical examples are given to illustrate the effectiveness and less conservatism of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Observer‐based Adaptive fuzzy control of time‐delay uncertain nonlinear systems

An observer‐based adaptive fuzzy model following controller is proposed for a class of MIMO nonlinear uncertain systems to cope with time‐delay, uncertainty in plant structure and disturbances. Based on universal approximation theorem the unknown nonlinear functions are approximated by fuzzy systems, where the premise and the consequent parts of the fuzzy rules are tuned with adaptive schemes. To have more robustness, and at the same time to alleviate chattering, an adaptive discontinuous structure is suggested. Moreover, the availability of the states measurement is not required and an adaptive observer is used to estimate the states. Asymptoic stability of the overall system is ensured using suitable a Lyapunov‐Krasovskii functional candidate. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

This paper considers the preview tracking control problem of polytopic uncertain discrete‐time systems with a time‐varying delay subject to a previewable reference signal. First, a model transformation is employed and a discrete‐time system with a time‐invariant delay and an external disturbance is obtained. The difference operator method can be extended to derive an augmented error system that includes future information on the reference signal. Then, a previewable reference signal is fully utilized through reformulation of the output equation while considering the output feedback. Based on the small gain theorem, a static output feedback controller with preview actions is designed such that the output can asymptotically track the reference signal. Finally, numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the paper.