Interval Stability and Stabilization of Linear Stochastic Systems

Abstract

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.