ℋ <sub>2</sub> state-feedback control for continuous semi-Markov jump linear systems with rational transition rates
Marcel de Almeida, Matheus Souza, André R. Fioravanti, O.L.V. Costa
Abstract
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.
Topics & Concepts
MathematicsMarkov chainJumpState (computer science)Control theory (sociology)Markov processLinear systemTransition rate matrixApplied mathematicsMarkov kernelMathematical optimizationMarkov modelComputer scienceControl (management)Variable-order Markov modelAlgorithmMathematical analysisStatisticsQuantum mechanicsArtificial intelligencePhysicsStability and Control of Uncertain SystemsAdvanced Control Systems OptimizationControl Systems and Identification