Sampled-data H ∞ control for a class of Markovian jump systems with input saturation via stochastic sampling design

• Published in: Transactions of the Institute of Measurement and Control Vol. 36; no. 3; pp. 291 - 299
• Main Authors: Li, Bo, Song, Xiaona, Zhao, Junjie
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.05.2014; Sage Publications Ltd
• Subjects: Input output; Markov analysis; Sampling techniques; Stochastic control theory; Markovian jump delayed systems; variable sampling; sampled-data system; H∞ control; input saturation
• ISSN: 0142-3312; 1477-0369
• DOI: 10.1177/0142331213497621

This paper deals with the problem of H ∞ control for a stochastic sampling Markovian jump system subject to input saturation. The stochastic sampling we address is a Bernoulli distribution and two different sampling periods are considered whose occurrence probabilities are known constants. Actually the control method in this paper can be applied to a system with multiple stochastic sampling periods. By transforming the original stochastic sampling Markovian jump system into a continuous Markovian jump delayed systems, the plant can be stabilized by a state-feedback controller with input saturation. By applying an appropriate Lyapunov–Krasovskii function, some sufficient conditions for the stabilization of the system and the H ∞ controller design are derived in terms of linear matrix inequalities. Finally, in order to validate the efficiency of the approach mentioned above, a simulation example is provided.