An Observer-Based Output Feedback Controller for the Finite-Time Stabilization of Markov Jump Linear Systems

In this letter, we investigate the finite-time output feedback control problem for continuous-time Markov jump linear systems. In this context, the first result is a sufficient condition for stochastic finite-time stability, requiring the solution of a feasibility problem constrained by differential linear matrix inequalities. Afterward, we consider the stabilization problem via output feedback dynamical controllers. The usual machinery pursued in the deterministic case would lead to stabilization conditions depending on differential bilinear matrix inequalities, that cannot be solved in practice. Therefore, a different methodology, based on the separation approach provided by Amato et al., is exploited to design an observer-based output feedback controller, which can be computed by solving an optimization problem depending on linear constraints. A non-trivial application example, involving the finite-time stabilization of the longitudinal dynamics of a helicopter, is presented in order to illustrate the effectiveness of the proposed technique.