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 (FIEED) for uncertain stochastic bilinear Markov jump systems based on the hidden Markov model (HMM). A more general performance index named as FILED 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-infinity, L-2 - L-infinity 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.

Automated summary

This paper investigates the finite-time exponentially extended dissipativity for uncertain stochastic bilinear Markov jump systems based on the hidden Markov model. It establishes sufficient conditions for the closed-loop system to satisfy the finite-time exponentially extended dissipative performance and proposes an asynchronous and robust resilient controller.