Finite-Time Stabilization of Uncertain Markovian Jump Systems: An Adaptive Gain-Scheduling Control Method

This article addresses the stochastic finite-time stabilization problem for a class of Markovian jump systems with polytopic uncertainties. First, an adaptive gain-scheduling-based control design method is well proposed. Compared with the traditional common/parameter-independent control method, the polytopic structure characteristic is well used via approximating uncertain parameters in controller design, which might reduce the conservatism and improve the flexibility of control design. Second, the controller gains and the transition rate matrix are codesigned to ensure the stochastic finite-time stability of the closed-loop system. Furthermore, an optimization problem is also established by minimizing the constrained upper bound of the system state to achieve the optimal closed-loop performance. Finally, two numerical examples are adopted to illustrate the effectiveness of the proposed method.