Static Output Energy-to-Peak Control for Semi-Markov Jump Linear Systems with Phase-Type Distributions and Hidden Modes

This paper studies the $L_{2}-L_{\infty }$ (also known as energy-to-peak) static output feedback control for continuous-time semi-Markov jump systems, with the jump times modeled through phase-type (PH) distributions. It is also assumed that the post-jump state variable of the semi-Markov model is not directly accessible and the controller has only access to an observed process related to this variable. The goal is to provide sufficient conditions for the design of static output feedback controllers satisfying an upper bound on the $L_{2}-L_{\infty }$ ratio in terms of Linear Matrix Inequalities (LMIs). Moreover, in order to reduce the $L_{2}-L_{\infty }$ upper bound ratio, a coordinate descent algorithm is also presented, starting from a feasible solution for the LMIs restrictions. Numerical examples are presented to illustrate the results.