Input-Output Approach to Control for Fuzzy Markov Jump Systems With Time-Varying Delays and Uncertain Packet Dropout Rate

• Published in: IEEE transactions on cybernetics Vol. 45; no. 11; pp. 2449 - 2460
• Main Authors: Zhang, Lixian, Ning, Zepeng, Shi, Peng
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.11.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation methods; Closed loop systems; Control systems; Controllers; Delay; Delay effects; Delays; Dropouts; Fuzzy; Fuzzy set theory; Gain; H∞ control; Markov jump systems; Markov processes; Robots; scaled small gain (SSG) theorem; Stability analysis; Takagi > Sugeno (T-S) fuzzy systems; time-varying delays; Time-varying systems; unreliable communication links; boldsymbol {H}_{\infty } control; Markov jump systems; scaled small gain (SSG) theorem; unreliable communication links; Takagi–Sugeno (T-S) fuzzy systems; time-varying delays
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2014.2374694

This paper is concerned with H ∞ control problem for a class of discrete-time Takagi-Sugeno fuzzy Markov jump systems with time-varying delays under unreliable communication links. It is assumed that the data transmission between the plant and the controller are subject to randomly occurred packet dropouts satisfying Bernoulli distribution and the dropout rate is uncertain. Based on a fuzzy-basis-dependent and mode-dependent Lyapunov function, the existence conditions of the desired H ∞ state-feedback controllers are derived by employing the scaled small gain theorem such that the closed-loop system is stochastically stable and achieves a guaranteed H ∞ performance. The gains of the controllers are constructed by solving a set of linear matrix inequalities. Finally, a practical example of robot arm is provided to illustrate the performance of the proposed approach.