Energy-to-Peak Filtering of Semi-Markov Jump Systems With Mismatched Modes

In this article, the problem of energy-to-peak filtering problem is studied for a class of continuous-time semi-Markov jump systems with mismatched modes. We consider the scenario where the mode of the system is not always instantaneously accessible and mismatches the mode of the filter. To cope with this asynchronous phenomenon, we introduce a hidden semi-Markov model and use a stochastic process as a switching signal of the filter to observe the system modes. By the Lyapunov function approach and linear matrix inequality method, sufficient conditions are developed to ensure the filtering error dynamics is stable with a prescribed energy-to-peak performance index. Two examples are given to illustrate the effectiveness of the proposed design technique.