Energy-to-Peak Static Output Control for Continuous-Time Hidden Markov Jump Linear Systems

Abstract

We study the L2 — L∞ static output feedback control, also known as energy-to-peak control, for continuous-time Markov jump systems in a context of partial observation of the Markov chain. We consider that the controller has only access to an observed process related to the Markov chain of the plant by means of an exponential hidden Markov model. Sufficient conditions for the design of output feedback controllers satisfying an upper bound on the L2—L∞ ratio are given in terms of Linear Matrix Inequalities (LMIs). Based on this result a coordinate descent algorithm is presented to reduce the L2—L∞ upper bound ratio, starting from a feasible solution for the LMIs restrictions. The paper is conclude with a numerical example to illustrate the results.