Guoping Lu

Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation

This note considers the generalized quadratic stability problem for continuous-time singular system with nonlinear perturbation. The perturbation is a function of time and system state and satisfies a Lipschitz constraint. In this work, a sufficient condition for the existence and uniqueness of solution to the singular system is firstly presented. Then by using S-procedure and matrix inequality approach, a necessary and sufficient condition is presented in terms of linear matrix inequality, under which the maximal perturbation bound is obtained to guarantee the generalized quadratic stability of the system. That is, the system remains exponential stable and the nominal system is regular and impulse free. Furthermore, robust stability for nonsingular systems with perturbation can be obtained as a special case. Finally, the effectiveness of the developed approach for both singular and nonsingular systems is illustrated by numerical examples.

Full-order and reduced-order observers for Lipschitz descriptor systems: the unified LMI approach

This brief considers a new observer design for a class of continuous-time descriptor systems with Lipschitz constraint. Both types of full-order and reduced-order observers are constructed by a unified linear matrix inequality (LMI) approach. Under the sufficient condition in the form of LMI, the errors are guaranteed to be exponentially convergent. An illustrative example is presented to show the effectiveness of the proposed approach.

Continuous stabilization controllers for singular bilinear systems: The state feedback case

Global asymptotic stabilization for a class of singular bilinear systems is first studied in this paper. New approaches are developed by means of the LaSalle invariant principle for nonlinear systems. A new set of sufficient condition is first derived via the continuous static state feedback, the feedback not only guarantees the existence of solution but also the global asymptotical stabilization for the closed loop system.

Nonlinear robust H∞ control via dynamic output feedback ☆

The problem on robust H∞ control for a class of nonlinear systems with parameter uncertainty is studied. Sufficient conditions for the existence of the dynamic output feedback controller are obtained. Under these conditions, the closed-loop systems have robust H∞-performance. A numerical example is given to illustrate the design of a robust controller using the proposed approach.

Brief paper: Detection and stabilization for discrete-time descriptor systems via a limited capacity communication channel

This paper addresses the state estimation and stabilization for linear discrete-time descriptor systems. It is assumed that the estimator and controller can only receive the transmitted sequence of finite coded signals via a limited digital communication channel. Both coder-decoder and coder-decoder-controller procedures are proposed, in which a compensation term is introduced to meet the compatible requirement. In addition, an effective method for selecting the compensation term is presented. Detection and stabilization conditions in terms of linear matrix inequality are obtained. Finally, an example is given to illustrate the effectiveness of design procedures.

Saturated Feedback Stabilization of Discrete-Time Descriptor Bilinear Systems

This note addresses global asymptotic stabilization of a class of discrete-time descriptor bilinear systems via a saturated state feedback controller. Based on LaSalle invariance principle and the implicit function theorem, sufficient conditions are presented to guarantee the uniqueness and existence of solution and the global asymptotic stability of the resulting closed-loop systems simultaneously. It is shown that the condition is independent of the state transformation for the given descriptor systems. Furthermore, the effectiveness of the proposed design method is illustrated by a numerical example.

Strict positive realness for linear time-delay systems

The strict positive realness (SPR) of a linear time-delay system via a linear matrix inequality (LMI) technique is studied. Presented are sufficient conditions via LMIs such that the linear delayed system is strictly positive real. More generally, we present a memoryless state feedback controller via LMIs such that the resulting closed-loop system is SPR with an α -asymptotic stability constraint (α -SPR) for a class of linear time-delay control systems. Furthermore, an LMI approach to the optimization problem of computation of the maximal allowable bound on the time delays is given such that the closed-loop system is α -SPR. Finally, a numerical example illustrates the effectiveness of the results.

Technical communique: A note on the existence of a solution and stability for Lipschitz discrete-time descriptor systems

This paper addresses the existence and uniqueness of a solution and stability for Lipschitz discrete-time descriptor systems. By means of the fixed point principle, a criterion is presented via a matrix inequality, and the criterion guarantees the existence and uniqueness of a solution. In addition, a sufficient condition is also presented to ensure that the solution exists for any compatible initial condition and the system is globally exponentially stable simultaneously. It is shown that the criterion presented in this paper is easy to verify and independent of the choices of decomposition matrices for the given system. Finally, the approach is illustrated by a numerical example.

Stabilization for Networked Control Systems with Nonlinear Perturbation

Abstract This paper discusses the stabilization controller designs for a class of networked control systems with nonlinear perturbation. Under consideration of both network-induced delay and the data packet dropout in the transmission, a state feedback controller and a static output feedback controller are constructed, respectively. In addition, the effectiveness of our approach is demonstrated by two numerical examples.

Passivity Analysis of Uncertain Singularly Perturbed Systems

This brief addresses the asymptotic stability and passivity of uncertain singularly perturbed systems. Based on the Lyapunov stability theory and a singular-system approach, some sufficient conditions in terms of linear matrix inequalities are derived. Three numerical examples are presented to demonstrate the effectiveness of the proposed theoretical results.