Robust l₂−l_∞ dynamic output feedback control design for uncertain discrete‐time switched systems with random time‐varying delay

Abstract

SummaryThis article deals with the problem of robust output feedback control design for a class of switched systems with uncertainties and random time‐varying delay. Our purpose is focused on designing a full order dynamic output feedback controller and an appropriate switching rule to ensure the exponential mean square stability of the resulting closed‐loop switching system with an l2−l∞ performance level. The appealing aspects of the proposed control scheme include: (a) the development of LMI based delay‐dependent sufficient conditions for the exponential stability analysis of the stochastic hybrid systems using the appropriate choice of the augmented Lyapunov–Krasovskii functional, the partitioning technique and the average dwell time, (b) conservatism reduction of the unified design conditions, and (c) the controller designed exhibiting robustness with l2−l∞ performance against uncertainties and external disturbance. Finally, representative examples are given to demonstrate the validity and the merit of the proposed design technique.

H∞ control for networked semi‐Markovian jump systems with generally incomplete transition probabilities and distributed delays

“…In Table 1, the method in References 32,34 with $$$ {h}_1=h $$$, $$$ {p}_1=1 $$$ is just the time‐varying delay case without considering delay distribution. It is seen that larger $$$ h $$$ is obtained by considering delay distribution in References 32,34, and larger $$$ h $$$ is obtained by $$$ m $$$‐subdivision method replace the 2‐subdivision of the time‐varying delay as used in Reference 33. However, all of them are confined to limited subinterval and delay probability distribution is depended on the cumulative probability, which cannot reflect real delay probability distribution while our delay probability density model can be more closely and get larger maximum allowable delay.…”

“…Consider the short delays for $$$ \eta \in \left[1,{h}_1\right] $$$ occurring in probability $$$ {p}_1\left(0\le {p}_1\le 1\right) $$$ and long delays for $$$ \eta \in \left[{h}_1,h\right] $$$ in probability $$$ 1-{p}_1 $$$, a delay distribution‐based approach is proposed in References 32,34, while in Reference 33 the delay interval $$$ \left[1,{h}_1\right] $$$ is divided into m subintervals and probability distributions of $$$ h $$$ in every subinterval is uncertain and sum values of probability is 1. Then, the maximum allowable delay bounds $$$ h $$$ that guarantee the stability of the system () by Theorem 1 and method in References 32‐34 are given in Table 1.…”

“…In summary, the main contributions of this paper are epitomized by the following three aspects: The resultant S‐MJNCSs (), which is developed by using the GITTPs and distributed delays, although the simultaneous consideration of those factors make the analysis and control synthesis more challenging and complicated, it reflect more practical circumstances. Aiming at describing the stochastic with high accuracy and broadening practical application background, S‐MJSs are used to relax the limitations of MJSs for depicting NCSs. Meanwhile, instead of completely known or incomplete TPs, 21,22 GITTPs of this article are assumed to be generally uncertain with two cases, one possible case is completely unknown, the other case is time‐varying but bounded with upper and lower bounds, which could suit for real industrial applications more closely. In comparison to References 32‐36, which utilize variables 32‐34 or fixed distribution 35,36 to represent delay probability distribution without fully taking advantage of delay distribution if it is available. Herein, a new discrete distributed time‐delay model is established via a density kernel function.…”

“…In comparison to References 32‐36, which utilize variables 32‐34 or fixed distribution 35,36 to represent delay probability distribution without fully taking advantage of delay distribution if it is available. Herein, a new discrete distributed time‐delay model is established via a density kernel function.…”

“…Specifically, the issue of less conservative robust stability for uncertain discrete stochastic singular systems with time‐varying delay is investigated in Reference 32, the delay‐range‐dependent and delay‐distribution‐independent stability problem for discrete‐time singular MJSs was studied in Reference 33. Amin et al investigated robust $$$ {l}_2-{l}_{\infty } $$$ dynamic output feedback control design for uncertain discrete‐time switched systems with random time‐varying delay in Reference 34. Nevertheless, the channel of using a variable to describe the delay distribution is depended on the cumulative probability, in which more concrete delay information, such as probability density, is not taken into account.…”