Annular Stochastic Finite-Time Stability Using Piecewise Quadratic Lyapunov Functions

In this letter we present some new sufficient conditions for the annular stochastic finite-time stability of a class of stochastic linear time-varying systems. These new conditions are obtained adopting time-varying piecewise quadratic Lyapunov functions rather than the classical quadratic ones. The proposed approach allows us to extend the class of consider domains, which are typically limited to ellipsoidal domains. The proposed finite-time stability conditions can be converted into a feasibility problem based on a set of differential linear matrix inequalities. Two numerical examples are considered to perform a comparison with the previous results, and they show that the new proposed conditions are less conservative than the previous ones.