Stabilization For Uncertain Singular Systems Research Articles

Stability analysis of uncertain singular systems

Uncertain singular system, described as a multi-dimensional uncertain differential equation, is a kind of singular system disturbed by canonical process. Stability analysis has been widely investigated while nobody has ever considered the stability of uncertain singular systems. In this paper, three different styles of stabilities called stability in mean, stability in measure and almost sure stability of uncertain singular systems are studied. These stabilities can be employed to illustrate the internal character of uncertain singular systems in different aspects. Several sufficient conditions are presented to judge the above stabilities. An example is given to show the effectiveness of the results obtained.

Delay-range-dependent Robust Stability for Uncertain Singular Systems with Interval Time-varying Delays

In this paper, we consider the delay-range- dependent robust stability problem of uncertain singular system with interval time-varying delays. Stability criteria, which guarantee the concerned singular system is regular, free and stable, is derived in terms of linear matrix inequalities (LMIs) by introducing some identical equations with integral inequality approach (IIA) and using the Leibniz-Newton formula to reduce the conservatism of the results. The upper bound of time-delay can be obtained by using the modified generalized eigenvalue minimization problem (GEVP) technique such that the system can be stabilized for all time-delays. Finally, numerical examples show the method presented in our paper is more effective and less conservative than the existing ones.

Admissibility analysis and control synthesis for descriptor systems with random abrupt changes

This article addresses the admissibility analysis and state-feedback robust control synthesis problem for a class of uncertain descriptor systems with time delays and Markovian jumping parameters. In particular, the delay factor is assumed to be time varying which belongs to a given interval and parameter uncertainties are assumed to be time-varying but norm bounded. By implementing linear matrix inequality optimization approach together with delay fractioning technique, a new set of delay dependent sufficient condition is derived which guarantees that the uncertain singular system to be regular, impulse-free and stochastically stable. Further, a static robust control design with an appropriate gain control matrix has been derived to achieve the robust stabilization for uncertain singular systems in the presence admissible parameter uncertainties and random abrupt changes. By considering the relationship among the time varying delay and its lower and upper bounds, a new set of sufficient conditions are established for the existence of state feedback control in terms of LMIs, which can be efficiently solved via MATLAB LMI toolbox. More precisely, when these LMIs are feasible, an expression of a desired static robust control will be determined. Further, numerical examples with simulation result are given to show that the obtained result significantly improve the allowable upper bounds of delays over some existing results.

Delay Dependent Robust Stability of Singular Systems with Additive Time-varying Delays

This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

Sliding Mode Control Design for Uncertain Singular Systems

This paper addresses the problem of sliding mode control design and adaptive sliding mode control design for robust stabilization of uncertain singular systems with guaranteed control performance. Based on the Lyapunov stability theorem, we solve two sufficient conditions for stabilization of the uncertain singular systems. The proposed sliding mode controller and adaptive sliding mode controller can reduce the effect of uncertainty. An electrical system is given to illustrate the validity of the proposed scheme. Simulation result shown that the adaptive sliding mode control design is better than sliding mode control design case.

Delay-dependent robust stabilization for uncertain singular systems with multiple time-varying state delays

In this note, the problem of delay-dependent robust stabilization for singular systems with multiple time-varying state delays has been investigated, and the problem is solved via state feedback controller in terms of a linear matrix inequality technique. Numerical examples are given to show the validity of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Delay-dependent Robust Stabilization for Uncertain Singular Systems with Multiple Input Delays

In this paper,the problem of delay-dependent robust stabilization is investigated for singular systems with multiple input delays and admissible uncertainties.First,an improved delay-dependent stabilization criterion for the nominal system is established in terms of linear matrix inequalities(LMIs).Then,based on this criterion,the problem is solved via state feedback controller,which guarantees that the resultant cloeed-loop system is regular,impulse free,and stable for all admissible uncertainties. Numerical examples are provided to illustrate the effectiveness of the proposed method.

Delay-dependent Robust Stabilization for Uncertain Singular Systems with Multiple Input Delays

Abstract In this paper, the problem of delay-dependent robust stabilization is investigated for singular systems with multiple input delays and admissible uncertainties. First, an improved delay-dependent stabilization criterion for the nominal system is established in terms of linear matrix inequalities (LMIs). Then, based on this criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free, and stable for all admissible uncertainties. Numerical examples are provided to illustrate the effectiveness of the proposed method.

Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays

This paper is concerned with exponential estimates and stabilization for a class of uncertain singular systems with discrete and distributed delays. A sufficient condition, which does not only guarantee the exponential stability and admissibility but also gives the estimates of decay rate and decay coefficient, is established in terms of the linear matrix inequality (LMI) technique and a new Lyapunov–Krasovskii functional. The estimating procedure is implemented by solving a set of LMIs, which can be checked easily by effective algorithms. Under the proposed condition, the algebraic subsystems possess the same decay rate as the differential ones. Moreover, a state feedback stabilizing controller which makes the closed-loop system exponentially stable and admissible with a prescribed lower bound of the decay rate is designed. Numerical examples are provided to illustrate the effectiveness of the theoretical results.

Delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays

This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality (LMI) approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closed-loop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.

Input-output approach to robust stability and stabilization for uncertain singular systems with time-varying discrete and distributed delays

Based on input-output approach, the robust stability and stabilization problems for uncertain singular systems with time-varying delays are investigated. The parameter uncertainties are assumed to be norm-bounded and the time-varying delays include both discrete delay and distributed delay. By introducing a new input-output model, the time-delay system is embedded in a family of systems with a forward system without time delay and a dynamical feedback uncertainty. A sufficient and necessary condition, which guarantees the system regular, impulse-free and stable for all admissible uncertainties, is obtained. Based on the strict linear matrix inequality, the desired robust state feedback controller is also obtained. Finally, a numerical example is provided to demonstrate the application of the proposed method.

Delay-dependent Robust Stabilization for Uncertain Singular Systems with State Delay

This paper considers the problem of delay-dependent robust stabilization for uncertain singular delay systems. In terms of linear matrix inequality (LMI) approach, a delay-dependent stability criterion is given to ensure that the nominal system is regular, impulse free, and stable. Based on the criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free, and stable for all admissible uncertainties. An explicit expression for the desired controller is also given. Some numerical examples are provided to illustrate the validity of the proposed methods.

An algebraic approach to the robust stability analysis and robust stabilization of uncertain singular systems

This paper considers the problems of robust stability analysis and robust stabilization for uncertain singular systems with norm-bounded time-varying uncertainties. The robust stability problem is solved via the notion of generalized quadratic stability which guarantees that the uncertain singular system is stable, regular and impulse free simultaneously for all admissible uncertainties, while the robust stabilization problem is solved via the notion of generalized quadratic stabilizability. An algebraic approach is adopted in the paper. Our main results are extensions of some existing results on uncertain regular systems for singular systems.