Asynchronous Finite-Time Exponentially Extended Dissipativity for Stochastic Bilinear Markov Jump Systems

In this paper, we are concerned with the finite-time exponentially extended dissipativity (FTEED) for uncertain stochastic bilinear Markov jump systems based on the hidden Markov model (HMM). A more general performance index named as FTEED is given to make the concept of extended dissipativity in infinite-time domain suitable for the finite-time case. With the help of the recursive technique and the stochastic Lyapunov functional method, sufficient conditions are established such that the closed-loop uncertain stochastic bilinear hidden Markov jump systems are finite-time stochastic bounded while satisfying the finite-time exponentially extended dissipative performance. The obtained results can be regarded as corresponding extensions of finite-time $H_\infty, L_{2}-L_\infty $ , passive, and dissipative control. Furthermore, an asynchronous and robust resilient controller is successfully derived for all the admissible bounded perturbations in terms of linear matrix inequalities (LMIs). Finally, a numerical example is used to demonstrate the effectiveness of proposed methods.