A linear matrix inequality (LMI) based criterion for the global asymptotic stability of discrete-time systems with multiple state-delays employing saturation nonlinearities is presented. Numerical examples highlighting the effectiveness of the proposed criterion are given.

When discrete-time systems are implemented in finite word length processor using fixed-point arithmetic, nonlinearities are introduced due to quantization and overflow. Such nonlinearities may result in the instability of the designed system. The global asymptotic stability of the null solution guarantees the nonexistence of limit cycles in the realized system. A number of researchers [

Time delays are generally encountered in various physical, industrial, and engineering systems due to measurement and computational delays, transmission, and transport lags [

Stability analysis of discrete-time systems in the simultaneous presence of nonlinearities and time delays in their physical models is an important problem.

This paper, therefore, deals with the problem of stability analysis of a class of discrete-time state-delayed systems in state-space realization employing saturation overflow arithmetic. The paper is organized as follows. Section

In this section, the description of the system under consideration is given. The following notations are used throughout the paper:

The system under consideration is given by

Let

A class of discrete-time systems can be described with (

The equilibrium state

In this section, a linear matrix inequality (LMI) based criterion for the global asymptotic stability of the system (

Suppose

For

Now, we have the following lemma.

The matrix

Using (

Now, we prove our main result.

The zero solution of the system described by (

Let

Consider a quadratic Lyapunov function [

From (

The matrix inequality (

Note that condition (

Condition (

Stability of the system can be established via Theorem

In this section, we will compare the main result of this paper with the result stated in [

The zero solution of the system described by (

Theorem

It can be easily conceived that, with

The present work may be treated as an extension of [

In this section, two numerical examples are given to demonstrate the usefulness of the present result.

Consider a second-order system (

We now apply Theorem

Trajectory for the state variables.

The global asymptotic stability of the system under consideration (via Theorem

Consider a system described by (

An LMI-based sufficient condition (Theorem

The potential extensions of the proposed idea to the problems of stability of linear discrete-time systems with interval-like time-varying delay in the state [

The author declares that there is no conflict of interests regarding the publication of this paper.

The author wishes to thank Professor Fernando Tadeo and the anonymous reviewers for their constructive comments and suggestions.