Stochastic stability properties of jump linear systems

• Published in: IEEE transactions on automatic control Vol. 37; no. 1; pp. 38 - 53
• Main Authors: Feng, X., Loparo, K.A., Ji, Y., Chizeck, H.J.
• Format: Journal Article
• Language: English
• Published: Legacy CDMS IEEE 01-01-1992; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control systems; Control theory. Systems; Controllability; Cybernetics; Exact sciences and technology; Linear systems; Optimal control; Stability; State feedback; Stochastic resonance; Stochastic systems; Sufficient conditions; Testing; Jump process; Stability; Linear system; Necessary and sufficient condition; Lyapunov exponent
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/9.109637

Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for delta -moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0/sup +/.< >