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

• Published in: International journal of robust and nonlinear control Vol. 30; no. 5; pp. 1956 - 1978
• Main Authors: Xie, Wenqian, Zhang, Ruimei, Zeng, Deqiang, Shi, Kaibo, Zhong, Shouming
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.03.2020
• Subjects: aperiodic sampling; Data transmission; Event triggered control; general transition rates; Markov jump systems; Stabilization; strict dissipativity
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4856

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.