Finite-time stability and stabilization of nonlinear stochastic hybrid systems

• Published in: Journal of mathematical analysis and applications Vol. 356; no. 1; pp. 338 - 345
• Main Authors: Yang, Ying, Li, Junmin, Chen, Guopei
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.08.2009; Elsevier
• Subjects: Brownian motion; Combinatorics; Combinatorics. Ordered structures; Designs and configurations; Exact sciences and technology; Finite-time stability; Global analysis, analysis on manifolds; Impulsive systems; Markovian switching; Mathematical analysis; Mathematics; Sciences and techniques of general use; Stabilization; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Brownian motion; Finite-time stability; Stabilization; Impulsive systems; Markovian switching; Closed loop; Partition; Impulsive system; Non linear system; Stochastic system; Hybrid system; Closed systems; Sufficient condition; Mathematical analysis; Feedback; Application; Numerical stability; Lyapunov function
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2009.02.046

This paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finite-time stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method.