A hybrid output feedback control scheme of Markovian jump systems via partly transition rates/probabilities design

The hybrid control scheme, involving the design of all transition rates/probabilities, has been extensively studied in the literature. However, there may be cases where certain transition rates/probabilities are fixed a priori, rendering existing methods inapplicable. In this paper, hybrid control schemes which consider the co-design of partly transition rates/probabilities and output feedback controller are respectively investigated for continuous-time and discrete-time Markovian jump systems by proposing a synchronous mode-dependent parametric method. Firstly, novel necessary and sufficient conditions are established to reconstruct the unfixed switching rates/probabilities that ensure the mean square stability of both continuous-time and discrete-time Markovian jump systems. Next, stabilization conditions are established via hybrid control design. Importantly, the decision matrices related to the fixed and unfixed transition rates/probabilities are strictly separated, resulting in reduced complexity demands and avoiding the requirement to solve complex parameters. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed methods.