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In this paper, we present a decentralized variable gain robust controller for a class of large-scale serially connected systems with nonlinear perturbations via piecewise Lyapunov functions. The nonlinear perturbation means the interconnections between the subsystems and uncertainties, and the proposed decentralized variable gain robust controller is designed so as to reduce the effect of uncertainties and interconnections. In this paper, on the basis of the concept of piecewise Lyapunov functions, we show sufficient conditions for the existence of the proposed decentralized variable gain robust controller. Finally, numerical examples are presented.

We present a framework for estimating states and parameters in systems that can be described by a detectable linear system perturbed by a nonlinear function of the states, exogenous signals, and a vector of unknown, constant parameters. The estimators designed in this framework consist of two interconnected modules: a parameter estimator that is constructed as though the states and the nonlinear perturbation were directly available for measurement; and an observer/perturbation estimator that estimates the states as well as the perturbation. The design methodology is based on satisfying an H ∞ condition, which leaves the designer with a wide range of options for carrying out the design. We discuss the use of LMI-based techniques in particular, and illustrate their application on a simulation example. We also discuss how the results of the paper can be applied to a more general class of cascaded nonlinear systems.

Author's version of a chapter published in the book: Proceedings of the 18th IFAC World Congress 2011. Also available from the publisher at: http://dx.doi.org/10.3182/20110828-6-IT-1002.03116

A feedback stabilization problem is investigated for a class of imperfectly known singularly perturbed time-delay systems of the neutral type, with discrete delays. The imperfections acting on the systems, which may be time-, state-, delayed state-, and/ or input-dependent, are modelled as additive nonlinear perturbations influencing a known set of nonlinear functional differential equations. Sufficient conditions, which include delay-dependent matrix inequalities, are presented and a class of robust feedback controls are designed to guarantee a prescribed stability property for the class of singularly perturbed systems.

In this paper, the problem of robust exponential stability for uncertain system with time varying delays and nonlinear perturbations is investigated. Using Lyapunov-Krasovskii functional, new delay dependent sufficient robust stability criteria is established in terms of Linear Matrix Inequality. Finally, numerical examples are considered to show the effectiveness of the developed approaches.

In this paper, synchronization of a directed network with Markovian jump (DNMJ) and nonlinear perturbations is considered. By analyzing the structure of the network, a pinning control scheme is given to ensure the synchronization of all nodes in a DNMJ. Finally, an example is provided to illustrate the effectiveness of the gained criterion.

This paper investigates the delay-dependent adaptive synchronization problem of the master and slave structure of linear systems with both constant neutral and time-varying discrete time-delays and nonlinear perturbations based on the Barbalat lemma and matching conditions. An adaption law which includes the master-slave parameters is obtained by using the Lyapunov functional method and inequality techniques to synchronize the master-slave systems without the knowledge of upper bounds of perturbation terms. Particularly, it is shown that the synchronization speed can be controlled by adjusting the update gain of the synchronization signal. A numerical example has been given to show the effectiveness of the method.

This note deals with the robust stability analysis for time-delay systems with nonlinear perturbations. Firstly, a new class of Lyapunov functional candidate is proposed to develop some new criteria by considering the additional useful terms and introducing some free-weighting matrices. Then, an augmented Lyapunov functional is introduced to establish a novel improved stability condition. All results obtained are given in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed methods.

This paper investigates the problem of the stabilization of uncertain time-delay systems containing saturating actuators. These uncertainties may be linear, nonlinear, and/or time-varying, but only the upper norm-bounds are known. The Lyapunov-Krasovskii technique is employed to analyze the stability robustness for the uncertain closed-loop system which is based on dynamical output feedbak controller. Some sufficient criteria addressing the robust stabilization of such systems are proposed. These conditions are shown to be an extention of those given by Han et al. (1998c) which are less restrictive than those given by Han and Mehdi (1998b) and Su et al. (1989).

This paper is concerned with a design of finite-dimensional H ∞ controllers for semilinear distributed parameter systems whose linear principal parts are of modal type. First, a finite-dimensional H ∞ controller is constructed for the linear distributed parameter system by using a previous result of the author. Then, it is shown that the finite-dimensional H ∞ controller works as a finite-dimensional H ∞ controller for the given semilinear distributed parameter system under certain conditions with respect to the nonlinear perturbation.

In this paper, earlier results are generalized for robust stability of delay systems with nonlinear time-varying perturbations. Sufficient conditions are stated in terms of the existence of some positive definite matrix functions satisfying certain Riccati-type equations to ensure the robust stability of the system.

The problem of robust stabilization for a class of delay differential systems with nonlinear perturbation is considered. Making use of the delay integral inequality and the technique of nonnegative matrix, the bounds of uncertain parameters are given by means of the spectral radius of a nonnegative matrix, Robustness conditions obtained in this paper involve the information of every nominal closed-loop eigenvalues and are less conservative than some previous results. A example is given to demonstrate the validity of the main results.

Sensitivity analysis of the general feedback synthesis problem for linear multivariable systems is presented. Both local linear and nonlocal nonlinear perturbation bounds are derived. Condition numbers for the general feedback synthesis problem and the pole assignment problem are given.

The question of stabilization of infinite dimensional control systems has occupied many control engineers and mathematicians. In this article we have obtained sufficient conditions for e-invariance for a class of systems by means of control input. A new technique is presented to prove that if the control is real, and 2π-periodic function having zero mean, then the solution of the system with control lies in an arbitrary small neighborhood of x =o for an unbounded interval of time for any nonlinear perturbations .