Hansheng Wu

Exponential stability of a class of nonlinear dynamical systems with uncertainties

Abstract Exponential stability for a class of nonlinear dynamical systems with uncertainties is investigated. Based on the stability of the nominal systems, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such a class of feedback controllers, we can guarantee exponential stability of uncertain nonlinear dynamical systems. Our approach can give a clear insight into system analysis. Finally, an illustrative example is given to demonstrate the utilization of the approach developed in this paper.

Stability and robust stabilization of nonlinear descriptor systems with uncertainties

In this paper, we consider the problems of stability and robust stabilization of nonlinear descriptor systems. Lyapunov stability theory for conventional systems is extended in a natural way to nonlinear descriptor systems, and some stability theorems for descriptor systems are given. By making use of the stability results on nonlinear descriptor systems developed above, we also discuss the robust stabilization problem of an important class of nonlinear descriptor systems with uncertain perturbations, and propose a class of stabilizing state feedback controllers for this class of uncertain descriptor systems.<<ETX>>

Decentralized output feedback control of large scale interconnected time-delay systems

The problem of decentralized output feedback stabilization of a class of large scale systems including time-varying delays in interconnections is considered. On the basis of the assumption that each isolated subsystem is strictly (feedback) positive real, we propose two classes of decentralized stabilizing output feedback controllers, i.e. linear and nonlinear, which can guarantee uniform ultimate boundedness and uniform asymptotic stability of large scale time-delay interconnected systems, respectively.

Lyapunov stability theory and robust control of uncertain descriptor systems

In this paper we consider the problem of stability and robustness of uncertain nonlinear descriptor systems. The Lyapunov stability theory for conventional systems is extended in a natural way to nonlinear descriptor systems, and some stability theorems for descriptor systems are given. By making use of the stability results developed in this paper, we also discuss the robust control problem of an important class of nonlinear descriptor systems with uncertainties, and propose a class of stabilizing state feedback controllers for this class of uncertain descriptor systems. Finally, a numerical example is given to demonstrate the utilization of our approach.

Decentralized robust control for a class of uncertain large-scale interconnected nonlinear dynamical systems

The problem of the decentralized robust control for a class of large-scale interconnected nonlinear dynamical systems with input interconnection and external interconnection perturbations is considered. Based on the stabilizability of each nominal isolated subsystem (i.e., the isolated subsystem in the absence of interconnection perturbations), a class of decentralized local state feedback controllers is proposed, and some sufficient conditions are derived by making use of the Lyapunov stability criterion such that uncertain large-scale interconnected systems can be stabilized asymptotically by these decentralized state feedback controllers. For large-scale systems with only input interconnection perturbations, such decentralized controllers become a class of decentralized stabilizing state feedback controllers. That is, the decentralized stability of such large-scale systems can be guaranteed always by using the decentralized state feedback controllers proposed in the paper. Finally, a numerical example is given to demonstrate the validity of the results.

Exponentially robust output tracking of SISO nonlinear systems with uncertainties

This paper is concerned with the problem of robust output tracking of uncertain single-input and single-output nonlinear systems. Based on Lyapunov method and input/output linearization approach for nonlinear state feedback synthesis, a continuous state feedback controller is proposed. Compared with the controllers reported in the control literature, the controller proposed in this paper can guarantee exponential stability instead of uniform asymptotic stability for the trajectory error system of nonlinear systems with uncertainties.

Robust stability of a class of uncertain nonlinear dynamical systems with time-varying delay

We consider the problem of robust stability of a class of uncertain nonlinear dynamical systems with time-varying delay. Based on the assumption that the nominal system (i.e. the system in the absence of uncertainty and delay) is stable, we derive some sufficient conditions on robust stability of uncertain nonlinear dynamical systems with time-varying delay. Some analytical methods and the Bellman-Gronwall inequality are used to investigate such sufficient conditions. The notable features of the results obtained in this paper are their simplicity in testing the stability of uncertain dynamical systems with delay and their clarity in giving an insight into system analysis. Our results are also applicable to perturbed time-delay dynamical systems without exact knowledge of the delay. In addition, a numerical example is given to demonstrate the validity of our results.

Exponential stabilization of SISO nonlinear systems with uncertainties

This paper is concerned with the problem of robust stabilization of uncertain single-input and single-output nonlinear systems. Based on the Lyapunov method and input/output linearization approach for nonlinear state feedback synthesis, a continuous state feedback controller is proposed. Compared with the controllers reported in the control literature, the controller proposed in this paper can guarantee exponential stability instead of uniform asymptotic stability for nonlinear systems with uncertainties.

Sufficient conditions for robust stability of large-scale dynamical systems including delayed states and parameter perturbations in interconnections

The problem of the robust stability of large-scale dynamical systems including delayed states and parameter perturbations in interconnections is considered. By using algebraic Riccati equations and some analytical methods, some sufficient conditions on linear decentralized state feedback controllers are derived so that the systems remain stable in the presence of delayed states and parameter perturbations. Such conditions give some bounds on the perturbations of interconnections with delayed states and uncertain parameters, and result in a quantitative measures of robustness for large-scale dynamical systems including delayed states and uncertain parameters in interconnections. The results obtained in this paper are applicable not only to large-scale systems with multiple time-varying delays, but also to large-scale systems without exact knowledge of the delays, i.e., large-scale systems with uncertain delays.

LQG Optimal Control System Design under Delayed Perturbations

Abstract This paper is mainly concerned with the problem of linear quadratic Gaussian (LQG) optimal control system design in the presence of uncertain perturbation and time–delay. For such a problem, some robust stability conditions are derived by making use of the conventional LQG theory and some analytical methods, which results in an approach to LQG optimal control design for linear stochastic dynamical systems with time–delay.