Robust Non-fragile Asynchronous Controller Design for Continuous-Time Markov Jump Linear Systems: Non-homogeneous Markov Process Approach

• Published in: Circuits, systems, and signal processing Vol. 37; no. 10; pp. 4234 - 4255
• Main Author: Faraji-Niri, Mona
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2018; Springer Nature B.V
• Subjects: Circuits and Systems; Computer simulation; Control systems design; Controllers; Electrical Engineering; Electronics and Microelectronics; Engineering; Instrumentation; Liapunov functions; Linear matrix inequalities; Linear systems; Markov analysis; Markov chains; Mathematical analysis; Matrix methods; Robust control; Signal,Image and Speech Processing; Transition probabilities; Vertical landing; Vertical takeoff; Uncertainty; Observed Markov chain; Linear matrix inequality; Non-homogeneous Markov process; Asynchronous control; Markov jump linear system; Non-fragility
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-018-0767-y

This paper proposes a robust asynchronous controller for continuous-time Markov jump linear systems (MJLSs). The asynchronous structure considers a case in which the Markov chain governing candidate controllers does not match the chain which manages the switching between system modes. This type of asynchronousy arises because the real-time, exact and precise detection of the system modes is not practical; therefore, the observed modes slightly differ with the actual modes. This paper models the asynchronousy through an additional, observed Markov chain which depends on the original Markov chain of the system according to uncertain transition probabilities. By this representation, the whole system is viewed as a non-homogeneous MJLS, and the sufficient stabilizability conditions as well as the controller gains are obtained through multiple mode-dependent Lyapunov functions. This approach leads to less conservative design results than the previous mode-independent schemes and proposes a much simple methodology to obtain the controller than the previous mode-dependent studies. For more generality, the proposed controller also takes the possible gain variations occurring in the implementation procedures into account and reports all the results in terms of linear matrix inequalities. Simulation results on a vertical takeoff and landing helicopter are presented and compared with the common mode-independent controller to illustrate the effectiveness of the developed method.