A Hybrid Sliding Mode Control Scheme of Markovian Jump Systems via Transition Rates Optimal Design
Zhiru Cao, Yugang Niu, James Lam, Xiaoqi Song
Abstract
This article investigates the hybrid sliding mode control problem for the uncertain Markovian jump systems (MJSs) via the transition rates optimal design. The stability condition for the transition rates is first established to ensure the exponential mean-square (EMS) stability of the unforced uncertain MJSs. Then the hybrid design strategy on the sliding mode controller and transition rate matrix is presented to ensure the EMS stability of the controlled system. Moreover, the iterative optimization algorithms are developed to acquire the desirable transition rates, control gain, and decay rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> . Finally, some numerical simulation results are provided.