Finite-time stochastic contractive boundedness of Markovian jump systems subject to input constraints. (January 2016)

• Record Type: Journal Article
• Authors: Cheng, Jun; Xiang, Huili; Wang, Hailing; Liu, Zhijun; Hou, Liyuan
• Is Part Of: ISA transactions. Volume 60(2016:Jan.)
• Page Start: 74
• Page End: 81
• Publication Date: 2016-01
• Subjects: Continuous time -- Finite-time stochastic contractive boundedness -- Linear matrix inequality -- Lyapunov–Krasovskii function; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2015.10.021
• Languages: English
• ISSNs: 0019-0578

Abstract

Abstract: This paper studies the finite-time stochastic contractive boundedness problem for a class of Markovian jump linear systems subject to input constraints. First of all, by employing exogenous disturbance, two novel concepts, namely finite-time stochastic contractive stability (FTSCS) and finite-time stochastic contractive boundedness (FTSCB) are introduced. Secondly, a relaxation scheme for incomplete (i.e., partly known, unknown, and uncertain) transition probability descriptions is introduced. Then, two kinds of design methodology of observer-based controllers are proposed. All the design conditions are established by employing a set of linear matrix inequalities (LMIs). At last, numerical examples are given to demonstrate the effectiveness of the proposed approach. Abstract : Highlights: FTSCS and FTSCB are introduced. The newly stochastic Lyapunov–Krasovskii functional and novel activation function conditions are proposed. A relaxation scheme for incomplete transition probability descriptions is introduced.