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Some new criteria of delay independent stability for the switched interval time-delay systems are deduced. The switching structure does depend on time-driven switching strategies. The total activation time ratio of the switching law can be determined to guarantee that the switched interval time-delay system is exponentially stable.

Switched systems constitute an important class of hybrid systems. Such systems can be described by a family of continuous-time subsystems (or discrete-time subsystems) and a rule that orchestrates the switching between them. It is well known that a wide class of physical systems in power systems, chemical process control systems, navigation systems, automobile speed change system, and so forth may be appropriately described by the switched model [

The state-driven switching method is that if all subsystems have the common Lyapunov function or the multiple Lyapunov functions, there are many choices of switching strategy to make the whole system stable. However, using these kinds of methods, the system must meet conditions completely. Therefore, the common Lyapunov function or the multi-Lyapunov function is difficult to construct for practical systems; even if we can construct the function, it is more complicated and not easy to implement on practical systems.

The time-driven switching method is based on the concept of dwell time [

Furthermore, the time-delay phenomenon also cannot be avoided in practical systems, for instance, chemical process, long distance transmission line, hybrid procedure, electron network, and so forth. The problem of time-delay may cause instability and poor performance of practical systems [

Basically, current efforts to achieve stability in time-delay systems can be divided into two categories, namely, delay-independent criteria and delay-dependent criteria. In this paper, in view of delay-independent analysis, we expect to aid in studying stability and designing time-driven switching law to achieve and implement in a practical switched interval time-delay system.

The following notations will be used throughout the paper:

First, consider the following switched time-delay system

Let us consider the switched interval time-delay system described by

Denote:

From the properties of matrix norm, we have

In this paper, we study the robust stability analysis and switching law design for the switched interval time-delay systems.

Some helpful lemmas and definitions are given below.

Consider the time-delay system:

In the light of Lemma

For matrices

Without loss of generality, we assume that the switched interval time-delay system (

Consider

Furthermore, we assume that

Suppose that the switched interval time-delay system (

By Lemma

From the previous inequality (

By Theorem

Consider the switched interval time-delay system with interval matrices.

From (

From (

In order to satisfy the switching law (

Trajectory response in Example.

We have developed methodologies for the delay-independent stability criteria of switched interval time-delay systems with time-driven switching strategy. On delay-independent stability analysis, the sufficient conditions of the switched laws are presented, and the total activation time ratio under the switching laws is required to be not less than a specified constant, such that the switched interval time-delay system is delay-independent and exponentially stable with stability margin. In addition, the main advantages of our approach showed that we can quantify the region of stability, extend to arbitrary subsystems of switched time-delay systems, and develop the simple time-driven switching rule to stabilize the switched interval time-delay systems.

This work is supported by the National Science Council, Taiwan, under Grants no. NSC 102-2221-E-218-017 and NSC100-2632-E-218-001-MY3.

_{2}gain analysis for switched symmetric systems with time delay