Interval Stability and Stabilization of Linear Stochastic Systems

• Published in: IEEE transactions on automatic control Vol. 54; no. 4; pp. 810 - 815
• Main Authors: Weihai Zhang, Weihai Zhang, Lihua Xie, Lihua Xie
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: alpha) -stability; alpha) -stabilization; Applied sciences; Asymptotic mean square stability; Automatic control; beta; Circuit faults; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Decay rate; Entropy; Exact sciences and technology; Fault detection; Filtering; Intervals; Lyapunov exponents; Process control; second-order moment Lyapunov exponent; spectrum assignment; Stability; Stabilization; Stochastic processes; Stochastic systems; Stochasticity; Second moment; second-order moment Lyapunov exponent; Probabilistic approach; Stabilization; Stochastic stability; Linear control; Asymptotic stability; Linear time invariant system; Uncertain system; (―β, ―α)-stability; Decay time; Asymptotic mean square stability; Lyapunov exponent; Linear matrix inequality; Stochastic control; spectrum assignment; Non deterministic system; (―β,―α)-stabilization
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2008.2009613

This technical note applies the spectrum technique to deal with the interval stability and stabilization of linear stochastic time-invariant systems. First, the notion of (-beta,-alpha) -stability of stochastic systems is defined and some relationships among the (-beta,-alpha) -stability, the decay rate of system state response, and the second-order moment Lyapunov exponent are revealed. We then address the (-beta,-alpha)-stabilization problem and give a sufficient condition via a linear matrix inequality approach.