Stabilization of interconnected nonlinear stochastic Markovian jump systems via dissipativity approach

• Published in: Automatica (Oxford) Vol. 47; no. 12; pp. 2796 - 2800
• Main Authors: Lin, Zhongwei, Liu, Jizhen, Zhang, Weihai, Niu, Yuguang
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.12.2011; Elsevier
• Subjects: [formula omitted] control; Applied sciences; Computer science; control theory; systems; Control system synthesis; Control systems; Control theory; Control theory. Systems; Dissipation; Dissipative systems; Exact sciences and technology; Inequalities; Markovian jumps; Mathematics; Nonlinear systems; Nonlinearity; Passivity; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Stabilization; Stochastic processes; Stochastic systems; Stochasticity; System theory; Markovian jumps; H ∞ control; Dissipative systems; Stochastic systems; Nonlinear systems; Markov process; Markovian system; Probabilistic approach; H infinite control; Non linear control; Feedback regulation; H; Systems theory; control; Non linear system; Passivity; Uncertain system; Hamilton Jacobi equation; Dissipative system; Global stabilization; Stochastic control; Jump process; Jumping; Non deterministic system
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2011.09.008

This paper considers the stabilization problems for interconnected nonlinear stochastic Markovian jump systems from the viewpoint of dissipativity theory. Based on the strongly stochastic passivity theory, the feedback equivalence and global stabilization problems are studied for interconnected nonlinear stochastic Markovian jump systems. The strongly stochastic γ -dissipativity sustains a direct H ∞ control for this class of systems instead of solving coupled Hamilton–Jacobi inequalities.