Reliable Output Feedback Control for Piecewise Affine Systems With Markov-Type Sensor Failure

• Published in: IEEE transactions on circuits and systems. II, Express briefs Vol. 65; no. 7; pp. 913 - 917
• Main Authors: Wei, Yanling, Park, Ju H., Qiu, Jianbin, Jung, Hoyoul
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loop systems; Control systems design; Convexity; Discrete time systems; Failure; Feedback control; Integrated circuit reliability; Liapunov functions; Linear matrix inequalities; Lyapunov methods; Markov chains; Mathematical models; mode-dependent piecewise Lyapunov function; Output feedback; Piecewise-affine systems; reliable control; Robustness (mathematics); Sensors; Vibration analysis
• ISSN: 1549-7747; 1558-3791
• DOI: 10.1109/TCSII.2017.2725981

This brief addresses the problem of robust and reliable <inline-formula> <tex-math notation="LaTeX">{\mathscr {H}_{\infty }} </tex-math></inline-formula> static output feedback (SOF) control for uncertain discrete-time piecewise-affine (PWA) systems with sensor failure in a descriptor system framework. The Markov chain is employed to describe the sensor failure behaviors. In particular, by utilizing a system augmentation approach, the conventional closed-loop system is initially converted into a descriptor PWA model. On the basis of a mode-dependent piecewise Lyapunov function, combined with S-procedure, a novel <inline-formula> <tex-math notation="LaTeX">{\mathscr {H}_{\infty }} </tex-math></inline-formula> performance analysis criterion is then presented. Furthermore, by some elegant linearization techniques, the PWA SOF controller design is proposed in terms of the feasibility of a convex optimization problem. Lastly, a numerical example illustrates the effectiveness and less conservatism of the proposed approach.