Extended Dissipativity-Based Control for Hidden Markov Jump Singularly Perturbed Systems Subject to General Probabilities

Abstract

This article deals with the extended dissipativity-based control issue for singularly perturbed systems (SPSs) with Markov jump parameters, in which the partial information issues of the Markov chain are fully considered. A comprehensive hidden Markov model (HMM) is established for the partial information issues on Markov chain, in which the transition probabilities of the hidden Markov state and the observation probabilities of the observed state are general, that is, the uncertainty and the unknown peculiarity of them may be encountered simultaneously. By using the HMM with general probabilities, a comprehensive criterion is derived to analyze the extended stochastic dissipativity of the hidden Markov jump SPSs with the different partial information issues on the Markov chain. Based on the derived criterion, an explicit expression to acquire the desired HMM-based controller is presented. An illustrative example and a vehicle active suspension system are, finally, show the validity of the established theoretical results.