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This paper deals with the problems of exponential admissibility and

Many real-world engineering systems always exhibit several kinds of dynamic behavior in different parts of the system (e.g., continuous dynamics, discrete dynamics, jump phenomena, and logic commands) and are more appropriately modeled by hybrid systems. As an important class of hybrid systems, switched systems consist of a collection of continuous-time or discrete-time subsystems and a switching rule orchestrating the switching between them and are of great current interest; see, for example, Decarlo et al. [

On the other hand, time delay is a common phenomenon in various engineering systems and the main sources of instability and poor performance of a system. Hence, control of switched time-delay systems has been an attractive field in control theory and application in the past decade. Some of the aforementioned approaches for nondelayed switched systems have been successfully adopted to hand the switched time-delay systems; see, for example, Du et al. [

Recently, a more general class of switched time-delay systems described by the singular form was considered in Ma et al. [

In this paper, we aim to solve the problem of

Throughout this paper, the superscript

Consider a class of switched singular time-delay system of the form

Since

For any

For any delay

regular if

impulse if

exponentially stable under the switching signal

exponentially admissible under the switching signal

The regularity and nonimpulsiveness of the switched singular time-delay system (

For the given

For switched systems with the average dwell time switching, the Lyapunov function values at switching instants are often allowed to increase

This paper considers both SF control law

Then, the problem to be addressed in this paper can be formulated as follows. Given the switched singular time-delay system (

First, we apply the average dwell time approach and the piecewise Lyapunov function technique to investigate the exponential admissibility for the switched singular time-delay system (

For prescribed scalars

The proof is divided into three parts: (i) to show the regularity and nonimpulsiveness; (ii) to show the exponential stability of the differential subsystem; (iii) to show the exponential stability of the algebraic subsystem.

(i) Regularity and nonimpulsiveness. According to (

(ii) Exponential stability of differential subsystem. Define the piecewise Lyapunov functional candidate for system (

(iii) Exponential stability of algebraic subsystem. Since

Now, following similar line as in Part 3 in Theorem 1 of Lin and Fei [

Theorem

Different from the integral inequality method used in our previous work [

If

Now, the following theorem presents a sufficient condition on exponential admissibility with a weighted

For prescribed scalars

Choose the piecewise Lyapunov function defined by (

Note that when

In this section, based on the results of the previous section, we are to deal with the design problems of both SF and SOF controllers for the switched singular time-delay system (

Applying the SF controller (

For prescribed scalars

According to Theorem

Scalars

Connecting the SOF controller (

For prescribed scalars

From Theorem

Note that there exist product terms between the Lyapunov and system matrices in inequality (

Matrices

In this paper, we have only discussed a special case of the derivative matrix

In this section, we present two illustrative examples to demonstrate the applicability and effectiveness of the proposed approach.

Consider the switched system (

Consider the switched system (

For SF control law, set

For SOF control law, let

The state trajectories of the open-loop subsystem 1.

The state trajectories of the open-loop subsystem 2.

Switching signal with the average dwell time

The state trajectories of the closed-loop system under SF control.

The state trajectories of the closed-loop system under SOF control.

In this paper, the problems of exponential admissibility and

This work was supported by the National Natural Science Foundation of China under Grant 60904020, Natural Science Foundation of Jiangsu Province of China (no. BK2011253), Open Fund of Key Laboratory of Measurement and Control of CSE (no. MCCSE2012A06), Ministry of Education of China, Southeast University, and the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (no. NY210080).