Class Of Singular Time-delay Systems Research Articles

H∞ Filtering for a Class of Singular Time-delay Systems

This paper describes the H∞ filtering problem for a class of nonlinear singular time-delay systems. A sufficient condition for the existence of H∞ filter is given. Based on the Cayley-Hamilton Theorem and Lyapunov stability theory, the H∞ filter is designed such that the filtering error is asymptotically stable and satisfies the prescribed H∞ performance. In terms of linear matrix inequality, a sufficient condition for the solvability of the addressed problem is obtained. Finally, some numerical examples are employed to demonstrate the effectiveness of the proposed approaches.

Dissipative control for singular time-delay system with actuator saturation via state feedback and output feedback

ABSTRACTThis paper is devoted to the problem of dissipative control for a class of singular time-delay systems with actuator saturation via state feedback and output feedback. First, by tuning the Wirtinger-based integral and the double integral inequality, a sufficient condition is derived to guarantee that the singular time-delay system is regular, impulse free, asymptotically stable and strictly (Q,S,R)-dissipative. Then, based on the derived condition, and applying linear matrix inequality techniques, the dissipative state feedback and output feedback controller are synthesised. Moreover, the maximal estimate of the domain of attraction is proposed by an optimisation problem. Finally, some simulation examples are provided to verify the effectiveness of the obtained theoretic results.

Non-linear observer design for a class of singular time-delay systems with Lipschitz non-linearities

In this paper, we consider a class of time-delay singular systems with Lipschitz non-linearities. A method of designing full-order observers for the systems is presented which can handle non-linearities with large-Lipschitz constants. The Lipschitz conditions are reformulated into linear parameter varying systems, then the Lyapunov–Krasovskii approach and the convexity principle are applied to study stability of the new systems. Furthermore, the observers design does not require the assumption of regularity for singular systems. In case the systems are non-singular, a reduced-order observers design is proposed instead. In both cases, synthesis conditions for the observers designs are derived in terms of linear matrix inequalities which can be solved efficiently by numerical methods. The efficiency of the obtained results is illustrated by two numerical examples.

Robust H∞ non-fragile control with memory state feedback for a class of singular time-delay systems

The problem of delay-dependent robust H∞ non-fragile control for a class of singular systems with state-delay and parameter uncertainties is investigated in this article. A delay-dependent sufficient condition for the problem of H∞ control for a class of singular systems is proposed by constructing the generalized Lyapunov–Krasovskii function, combining with linear matrix inequality approach. A memory state feedback controller under controller gain perturbations is obtained, which guarantees that, for all admissible uncertainties, the resulting closed-loop system is regular, impulse free, and stable with an H∞ disturbance attenuation level. Numerical examples show that the proposed methods are less conservative than existing ones.

Finite-time stability and stabilization of singular state-delay systems using improved estimation of a lower bound on a Lyapunov-like functional

Abstract In this paper, the problems of finite-time stability and stabilization for a class of singular time-delay systems are studied. Using the Lyapunov-like functional (LLF) with (exponential or power) weighting function and a new estimation method for the lower bound on LLF, some sufficient stability conditions are introduced. It is shown that the weighting function significantly reduces the conservatism of the stability criteria in comparison to estimation of the lower bound on LLF without this function. To solve the finite-time stabilization problem, a stabilizing linear state controller is designed by exploiting the cone complementarity linearization algorithm. Two numerical examples are given to illustrate the effectiveness of the proposed method

A neutral system approach to stability of singular time-delay systems

This paper is concerned with the problem of delay-dependent stability for a class of singular time-delay systems. By representing the singular system as a neutral form, using an augmented Lyapunov–Krasovskii functional and the Wirtinger-based integral inequality method, we obtain a new stability criterion in terms of a linear matrix inequality (LMI). The criterion is applicable for the stability test of both singular time-delay systems and neutral systems with constant time delays. Illustrative examples show the effectiveness and merits of the method.

Robust passive control for a class of singular time-delay systems with uncertainties

In the paper, the notion of passive uncertainties is proposed for uncertain singular systems under the state space. The robust passive control problem for a class of singular time-delay systems with uncertainties is discussed by using the linear matrices inequalities (LMIs), the sufficient condition of strictly passivation is obtained, and the robust passive controller for this class of uncertain singular systems is given. Finally, the feasibility of the theorems is shown by the numerical example.