H‐infinity fault‐tolerant control for Markov jump system with actuator time delay

Abstract

This study investigates H-infinity fault-tolerant control for Markov jump systems with actuator time delay. The main objective is to obtain some theorems such that the corresponding Markov jump systems with actuator time delay to be H-infinity stable and with some fault-tolerant performances. First, based on an integral transformation, the Markov jump systems with actuator time delay are described in a system description with a distributed time-delay item. Second, based on utilizing the linear matrix inequality theory, a positive energy functional, which includes a double integral item, is constructed. Then, after some mathematical operations, a sufficient condition is obtained for the Markov jump systems with actuator time delay to be H-infinity stable. If the condition is solvable, faulttolerant controller can be gotten to guarantee the controlled system to be H-infinity stable no matter there are some actuator faults existing in the system or not. Finally, examples are given to show the usefulness of the obtained theorem.

Finite-time energy-to-peak control for Markov jump systems with pure time delays

“…However, by setting p 11 =À 0:2, a = 1, b i1 = b i3 = 1, and b i2 = 0:5, we can obtain the maximum t = 1:119 by Theorem 3 in this study. Some more comparisons are given in Table 1, and the maximum values of t obtained in this study are much higher than those obtained in references, 36,[47][48][49][50] moreover, we can obtain a satisfactory result by tuning the value of a. In other words, the results obtained in this study are less conservative than those in references.…”

“…In other words, the results obtained in this study are less conservative than those in references. 36,[47][48][49][50] ! and some distributed time delay items.…”

“…This system was considered by Li et al 49 Reference 47 showed that when π 11 = − 0 . 2 , the maximum value of τ is 0.352, the maximum values of τ in references 36,48–50 are 0 . 822 , 0 . 848 , 1 . 002 , and 1 . 079 , respectively. However, by setting π 11 = − 0 . 2 , α = 1 , β i 1 = β i 3 = 1 , and β i 2 ...…”

“…In other words, the results obtained in this study are less conservative than those in references. 36,47–50…”

Adaptive fault‐tolerant decentralized tracking control of switched stochastic uncertain nonlinear systems with time‐varying delay

“…Time-delay is one of the main reasons for the deterioration or even instability of the overall performance of the system. [35][36][37][38][39][40][41][42][43][44][45] In most cases, stability is the premise for the normal operation of the system. Therefore, the stability research of time-delay systems has attracted great attention of researchers.…”