ℋ ₂ state-feedback control for continuous semi-Markov jump linear systems with rational transition rates

This paper presents the H2 State-Feedback Control for Continuous Semi-Markov Jump Linear Systems where the transition rates are given by the ratio of polynomials of the sojourn time. We show that, for instance, Rayleigh-, Erlang- and a class of Weibull-distributed sojourn time can be described by such a model. We present general results on the stability and on the H2 of Semi-Markov Jump Linear Systems and provide sum-of-squares conditions for norm calculation and state-feedback control design problems. We conclude the paper by presenting two numerical examples that point out the main features of our results and by discussing future directions and related problems.