The reliable

Singular systems [

Performance analysis has grown, in the past few decades, as one of the most important problems in control theory in addition to stability analysis. Many control problems, to a certain extent, can be equal to designing proper controller such that the closed-loop system is asymptotical stable and its performance satisfies some requirements. The general adopted performance indexes include

Motivated by the above discussion, in this paper, we focus on a generalized framework for reliable nonlinear

Throughout this paper,

Consider the following nonlinear discrete-time singular time-delay system described by

In this paper, we assume that

We also assume that the system (

Firstly, we consider the autonomous discrete-time singular time-delay system of (

The pair (

For system (

If set

When the actuators experience failures, we use

Considering the controller physical implementation convenience in the practical engineering, here, we are interested in a normal controller (

Define the augmented vector

With the aforementioned operator and system (

The objective of this paper is to design a general nonlinear dynamic output feedback controller of the form (

the closed-loop system (

under the zero-valued initial state condition, for any nonzero disturbance input

Firstly, a generalized stability criterion for discrete-time nonlinear singular system is proposed in this section. And then, based on this obtained result, a sufficient condition for the existence of a desired full-order

In this subsection, we concentrate our attention on the problems of system admissibility containing regularity, casuality, and stability and

For any nonlinear function

Firstly, we will prove the regularity and casuality of system (

Next, in order to show the stability of system (

In the sequel, we will focus on the

Given a positive scalar

Firstly, it is easy to see that

By introducing two slack matrix variables

Theorem

Given scalars

The matrices

Setting

yields

Then, from (

By Schur complement again, we have that

In this paper, the reliable

In this section, we give a numerical example to illustrate the effectiveness of the obtained controller design method. Consider the nonlinear singular system (

By applying the minimization problem in (

A generalized

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

This work was supported by the National Natural Science Foundation of China (61203143) and Young Teacher Training Program of Shanghai (slg11005).