Stochastic stability theory for systems containing interval matrices

Abstract

Known conditions for the stability of stochastic, linear time-varying (LTV) dynamical systems based on Liapunov theory are applied to LTV dynamical systems containing interval matrices; both discrete and continuous time processes are considered. These conditions are sufficient for stability with probability 1 (wp1) and, in the case of discrete time, also necessary for stability in m.s. They lead to a simple, noniterative technique that involves the computation of eigenvalues of matrices whose elements often consist of first- and/or second-order moments. The results are useful in areas such as robust design, feedback control, perturbation analysis, and fault tolerant systems.