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This paper focuses on the problems of static output feedback control and

Recently, there has been an increasing interest in the study of switched systems because a wide class of nonlinear systems are naturally written as switched systems [

There are a large number of literatures about the stability analysis and design of switched systems during the last few years [

Path-following method, which is an effective method for solving the biconvex optimization problem, was proposed by Hassibi et al. [

In this paper, the problem of static output feedback (SOF) control for discrete-time switched systems is studied. Based on piecewise quadratic Lyapunov functions [

This paper is organized as follows. Section

Consider the discrete-time switched system:

We study the problem of designing a static output feedback controller:

The following lemmas give the stability condition of closed-loop systems (

If there exist matrices

If there exists a fixed point

In this section, based on a piecewise quadratic Lyapunov function and the new linearization method, we will give new sufficient conditions for solving this problem.

If there exist points

By Schur complement, (

Thus, by Lemma

With Theorem

In

Consider the discrete-time switched system:

With the controller (

In this section, new sufficient conditions for SOF control design for the switched system (

The

Consider the switched system (

Obviously, inequality (

Now, the sufficient conditions to obtain SOF control gains with

If there exist points

By Schur complement, inequalities (

Write

That is, the following inequalities hold:

Thus, by Lemma

With Theorem

Based on Theorems

Consider the following.

Firstly, let

If

If

If

The wide perturbation step is a crucial step in improved path-following method. The purpose of this step is to broaden the search scope during each iteration so that the algorithm has the opportunity to escape form the local optimum. However, the enlarged search scope may cause nonconvergence. So the iteration number of wide perturbation step should not be too large. As long as the objective function

In this section, two examples are given to show the effectiveness of our method. Example

Consider system (

Consider a system with the following parameters:

Using our method, set

This paper studies the problems of static output feedback control and

Important future research work will be applying the results to some real-world systems. How to reduce the design conservatism is an important research topic that deserves further investigation.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported in part by the National Natural Science Foundation of China (nos. 61174033 and 61473160) and in part by the Natural Science Foundation of Shandong Province, China (ZR2011FM006).