State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties

• DOI: 10.1016/j.automatica.2014.10.065
• Publication Date: 2014-10-31T19:29:41Z
• Authors: Fanbiao Li; Ligang Wu; Peng Shi; Cheng-Chew Lim
• Keywords: Observer (physics); Mode (computer interface)

This paper is concerned with the state estimation and sliding mode control problems for phase-type semi-Markovian jump systems. Using a supplementary variable technique and a plant transformation, a finite phase-type semi-Markov process has been transformed into a finite Markov chain, which is called its associated Markov chain. As a result, phase-type semi-Markovian jump systems can be equivalently expressed as its associated Markovian jump systems. A sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated Markovian jump systems satisfy the reaching condition. Moreover, an observer-based sliding mode control problem is investigated. Sufficient conditions are established for the solvability of the desired observer. Two numerical examples are presented to show the effectiveness of the proposed design techniques.