Strictly dissipative stabilization of multiple‐memory Markov jump systems with general transition rates: A novel event‐triggered control strategy

Abstract

Summary This paper investigates the strictly dissipative stabilization problem for multiple‐memory Markov jump systems with network communication protocol. Firstly, for reducing data transmission, we put forward a novel mode‐dependent event‐triggered communication scheme based on aperiodically sampled data. Secondly, a Markov jump system with general transition rates is considered to make the result more applicable, where the transition rates of some jumping modes allow to be completely known, or partially known, or even completely unknown. Thirdly, a less restrictive Lyapunov‐Krasovskii functional, which is only required to be positive definite at end points of each subinterval of the holding intervals, is first introduced for event‐triggered control issue. Based on the above methods, a sufficient condition with less conservatism is obtained to ensure the stochastic stability and dissipativity of the resulting closed‐loop system. Meanwhile, an explicit design method of the desired controller is achieved. Finally, two numerical examples are presented to demonstrate the effectiveness and advantage of the proposed method.

Hybrid Event-Triggered Filtering for Nonlinear Markov Jump Systems With Stochastic Cyber-Attacks

“…jκ , E jk (κ ∈ {p, m}) and any invertible matrix K 13 , such that ∀i, j ∈ N (j > i), p, m ∈ M, (15) and the following linear matrix inequalities (LMIs) hold:…”

“…As stated in [13], if a positive minimum inter-event time can not be ensured, an infinite number of events maybe generated in a finite time interval, which is so-called Zeno behavior [14] and make the ETCM of no practical significance. Therefore, sampled-data-based ETCM has been proposed to exclude the Zeno behavior [15]- [19]. For example, the authors in [17] proposed a discrete ETCM that depends on nonuniformly sampled state to investigate the stabilization problem of neural-network-based control systems, the triggering condition is only verified at some nonuniform sampling instants.…”

An Improved Fuzzy Event-Triggered Asynchronous Dissipative Control to T–S FMJSs With Nonperiodic Sampled Data

“…Based on the HMM, a new AFETC is constructed to save the limited communication resource as compared to the published results [30]- [33]. It is noted that if N † = {1}, the AFETC is converted to the case investigated by [31], [32], while when N † = {1, 2, .…”

“…(ii) A new AFETC based on the HMM and nonperiodic sampled data is constructed to save the limited communication resource as compared to the published results [30]- [33], where the network-induced delays randomly occur.…”

An Improved Protocol to Consensus of Delayed MASs With UNMS and Aperiodic DoS Cyber-Attacks

“…Meanwhile, due to the failures of the link, packet drops, and abrupt environmental disturbances, the topology of the network may experience abrupt changes in its parameters and structure. Therefore, to tackle the consensus problem of MASs with Markov switching topologies (MSTs) [14], [15] is still an open challenge. Early works have successfully built a good theory for MASs with MSTs for which the transition rates (TRs) are completely known, which can be found in [16]- [18].…”