This paper concentrates on

Singularly perturbed systems widely exist in industrial processes, such as aircraft and racket systems, power systems, and nuclear reactor systems. These kind of systems usually embrace complicated dynamic phenomena which are characterized by slow and fast modes with multiple time-scales. This property causes high dimensionality and ill-conditioning problems. In control theory, a parameter-related state-space model is frequently used to describe a singularly perturbed system. With important practical meaning, the stability bounds of the singular perturbation parameter have been extensively studied by many researchers. In early times, a traditional method of decomposing the original system into fast and slow subsystems was frequently used, see [

In recent years, computer science is increasingly applied to industrial processes. Therefore, discrete-time singularly perturbed systems have attracted much attention. An

Though state feedback can achieve desired properties, it requires the availability of all state variables, which cannot be satisfied in most of the practical systems. On the other hand, dynamic output feedback usually increases the dimension of the original system. Therefore, static output feedback plays an important role in control theory considering that it is the simplest control technique in a closed-loop sense and can be easily realized with a cost not as high as that in state feedback case [

Based on those reasons and motivated by the above studies, we aim to design an

The rest of this paper is organized as follows. Section

The following notation will be adopted throughout this paper.

In this paper, we consider a class of linear fast sampling discrete-time singularly perturbed systems of the following form:

In the rest of this paper, we will assume that system (

The

The following lemmas will be used in establishing our main results.

Consider a discrete-time transfer function

there exists

holds.

The following two statements are equivalent.

Let

is feasible in

Let

holds.

The following two statements are equivalent.

Let

is feasible in

Let

hold.

In this section, two LMI-based methods of designing a static output feedback controller are proposed to ensure asymptotical stability of a closed-loop discrete-time singularly perturbed system (

Before giving the results, let

For a discrete-time singularly perturbed system in the form of (

Based on Lemma

where

To turn (

Applying Lemma

Both the static output feedback gain matrix

Note that the result in Theorem

Given a scalar

According to Lemma

Pre- and post-multiplying (

To turn (

Taking Lemma

From the above analysis, we learn that if there exists

We can obtain the static output feedback controller gain matrix

The result in Theorem

In this section, a numerical example is presented to illustrate the effectiveness of the proposed results.

Consider a discrete-time singularly perturbed system described by (

Though the performance of the closed-loop system is not as good as the state feedback case, static output feedback controller plays more important role in implemental sense with proper performance.

In this paper,

This work is supported by the National 973 Program of China (2012CB821202) and the National Natural Science Foundation of China (61174052, 90916003).