Optimized hybrid design with stabilizing transition probability for stochastic Markovian jump systems under hidden Markov mode detector

The transition probability synthesis problem is addressed for discrete‐time Markovian jump linear system (MJLS) with state‐dependent multiplicative noises. The proposed mode‐dependent parametric approach is employed to derive the necessary and sufficient condition for ensuring the existence of the stabilizing transition probability matrix (TPM). A key feature here is that the system mode is considered to be unavailable to the controller but can just be observed via a hidden Markov mode detector. To this end, a hybrid design is developed by co‐designing the stabilizing TPM and the asynchronous mode‐dependent state‐feedback controller. A rank‐constrained nonconvex problem is formulated to solve the hybrid design strategy. Specifically, a binary genetic algorithm (GA) is introduced for overcoming the computation difficulties arising from searching optimized mode‐dependent parameters. Finally, two numerical examples are provided to verify the effectiveness and advantages of the proposed hybrid design strategy via GA.