The observed mode dependent controller design problem for a class of continuous‐time hidden semi‐Markov jump systems

Summary This paper studies the stability analysis and stabilization synthesis problems for a class of continuous‐time jump systems with hidden system modes. To precisely model the switching signals of the considered systems, a novel definition of continuous‐time hidden semi‐Markov process is proposed based on the notions of emission probability and time varying dual‐index transition rate. By virtue of such definition, a dual‐index Lyapunov function is utilized to derive the sufficient stability conditions of the considered systems. By adopting a technology that can decouple the nonlinear terms in the above conditions, the numerically testable existence conditions of the controller for the resulting stabilizing systems are presented. An example is given to illustrate the effectiveness of our results.