Robust adaptive sliding mode control for uncertain delta operator systems

Abstract

In this paper, a robust adaptive sliding mode controller is presented for delta operator systems with mismatched uncertainties and exogenous disturbances. The parameters of the delta operator system are taken for norm-bounded uncertainties. The exogenous disturbance is also assumed to be bounded. After the statement of a sufficient condition for the existence of linear sliding surface based on linear matrix inequality technique, a robust reaching motion control method for delta operator systems is presented. Afterwards, an adaptive sliding mode controller for delta operator systems is designed. A bridge between the robust adaptive sliding mode control and the delta operator system framework is made. Numerical example is given to illustrate the effectiveness of the developed techniques.

Stability of genetic regulatory networks with time-varying delay: Delta operator method

“…Lemma 1 (Yang et al [30]). The property of delta operator for any time function xðtÞ and yðtÞ can be represented as δðxðtÞyðtÞÞ ¼ δxðtÞyðtÞþxðtÞδyðtÞþTδxðtÞδyðtÞ;…”

“…Definition 1 (Yang et al [30]). A delta operator system is asymptotically stable, if the following conditions hold:…”

Observer-based sliding mode control for a class of discrete systems via delta operator approach

“…References Contributions [16] Sliding mode observer for discrete systems [17] Sliding mode observer for continuous systems [6,7] SMC for delta operator systems This paper Sliding mode observer for delta operator systems…”

“…Therefore, the delta operator method is significantly less sensitive than the standard shift operator method at high sampling rate. A little results have been reported on SMC by using delta operator in literatures, such as time delay system SMC [6], adaptive SMC [7]. However, to the best of the authors' knowledge, the sliding mode observer for delta operator systems has received little attention now.…”

Soft sliding mode controller design for uncertain delta operator systems

“…State observer design for delta operator SMC system is obtained in [32]. Delta operator time-delay sliding mode controller with uncertainties is given in [33,34]. The research findings of soft sliding mode controller design for delta operator systems are relatively few.…”