H_∞ static output feedback control for singularly perturbed persistent dwell‐time switched systems with time‐varying delay and deception attacks

Abstract

This paper studies the static output feedback control issue for discrete-time singularly perturbed switched time-delay systems subject to randomly occurring deception attacks, in which the sequence for activated subsystems is governed by the persistent dwell-time switching strategy. The practical present phenomena that parameters alternately switch in fast or slow frequencies are characterized suitably with such strategy. Meanwhile, the deception attacks are assumed to occur in a random way that obeys the Bernoulli distribution. Moreover, some sufficient conditions are established by means of the Lyapunov stability theory, which guarantee the closed-loop system is mean-square exponentially stable with a prescribed  ∞ performance. Furthermore, based on the matrix processing technology, the desired controller gains are obtained. Finally, the rationality and effectiveness of the proposed method are verified by a numerical example.

H∞ synchronization of Markov jump neural networks with MPDT switching transition probabilities under DoS attacks

“…Ω ( k q p , k q p+1 ) denotes the switching times within [ k q p , k q p+1 ) . For arbitrary interval [k, t), inspired by Song et al [22], it holds that…”

“…$$$ \Omega \left({k}_{q_p},{k}_{q_{p+1}}\right) $$$ denotes the switching times within $$$ \left[{k}_{q_p},{k}_{q_{p+1}}\right) $$$. For arbitrary interval $$$ \left[k,t\right) $$$, inspired by Song et al [22], it holds that $$$$ \Omega \left(k,t\right)\le \left(\frac{t-k}{T+{\tau}_i}+1\right)\left(T+1\right). $$$$ …”

“…These works promote the study of time-varying TPs of MJNNs to a certain extent, but there still exists limitations because the DT switching rule requires the running time of each subsystem to be no less than a given value, and ADT switching rule is limited in the frequency of fast switching. Although the PDT switching TPs is introduced to relax restrictions of the ADT switching TPs and the DT switching TPs, there is only one common dwell time for time-varying TPs under PDT switching rule [22]. In some cases, the dwell time for time-varying TPs may not be consistent and the dwell time may be different for different subsystems [23][24][25].…”

Is exponential stability achievable in singular perturbed delayed systems with time-varying parameters? A comprehensive analysis

“…The stability properties of singular perturbed systems and the consequences of delayed dynamics have been the subject of extensive investigation in numerous studies [ [51] , [52] , [53] , [54] , [55] ]. Traditional methodologies employed in these studies have commonly assumed exponential stability in the fast subsystem, yielding valuable insights across diverse contexts [ [56] , [57] , [58] ].…”

H∞ control of switched Lurie systems with dwell time

“…13 Furthermore, based on the dwell time and multiple Lyapunov function method, some classical results for L 2 -gain and H ∞ control of switched systems were obtained. 14–16 Recently, the research on H ∞ performance involves more and more complex problems and more extensive fields, for instance, H ∞ control of singularly perturbed switched systems via output feedback, 17 finite-time H ∞ filtering of networked switched systems, 18 finite-time H ∞ bumpless transfer control of switched systems with state-dependent switching, 19 and so on.…”