Antidisturbance Control for Hidden Markovian Jump Systems: Asynchronous Disturbance Observer Approach

This article investigates the antidisturbance control issue for a class of Markovian jump systems with matched/mismatched disturbances by using disturbance observer approach. A key feature here is that the external disturbance is considered to be generated by a Markovian jump exogenous dynamics, in which the disturbance mode may not be synchronized with the system mode. Meanwhile, it is supposed that both system and disturbance modes can just be estimated via a hidden Markov mode detector. To overcome the possible obstacle in handling dual hidden Markov modes, a mapping technique for continuous-time Markov chain is provided first. Then, a novel asynchronous disturbance observer is developed to estimate the external disturbance by utilizing the detected mode. Based upon the estimated disturbance, asynchronous antidisturbance controllers are investigated for matched and mismatched disturbance cases, respectively. By employing a decoupling technique with the idea of completing the square, sufficient conditions are established for guaranteeing the stability in probability of the resultant closed-loop systems. Finally, two numerical examples are provided to verify the effectiveness of the proposed asynchronous antidisturbance control approaches under inaccessible system and disturbance modes.