Dissipativity-based resilient asynchronous control for Markov jump systems with sector-bounded nonlinearities. (June 2018)

• Record Type: Journal Article
• Authors: Zhang, Yujie; Liu, Xiujuan; Jiang, Junxia; Xiao, Yongshan
• Is Part Of: Transactions of the Institute of Measurement and Control. Volume 40:Number 9(2018)
• Page Start: 2821
• Page End: 2830
• Publication Date: 2018-06
• Subjects: Dissipativity -- Markov jump systems -- resilient asynchronous controller -- sector-bounded nonlinearity; Automatic control -- Periodicals; Measuring instruments -- Periodicals; Commande automatique -- Périodiques; Mesure -- Instruments -- Périodiques; 681.2
• DOI: 10.1177/0142331218765295
• Languages: English
• ISSNs: 0142-3312

Abstract

The resilient asynchronous dissipative control problem for Markov jump systems with sector-bounded nonlinearities in the discrete-time domain are examined in this study. The jumps between the system modes and controller modes are considered to be nonsynchronous. The mode transition of the controllers is governed by a nonstationary Markov chain, which can model the asynchronous jumps to different degrees that are also mode-dependent. The nonlinear functions are assumed to belong to sector sets with arbitrary boundaries. The sector boundaries can have positive and/or negative slopes, and therefore, we cover the most general case in our approach. Using the special structure of the system and by constructing a new multiple Lyapunov function, sufficient conditions regarding the existence of desired resilient asynchronous dissipative controllers are obtained in terms of linear matrix inequalities, which ensure the closed-loop system is stochastically stable and strictly dissipative. The designed controller can tolerate additive uncertainties in the controller gain matrix, which results from controller implementations. A numerical example is presented to show the effectiveness of the proposed theoretical results.