Static Output Constrained Control for Discrete-Time Hidden Markov Jump Linear Systems

This paper studies the static output quadratic control problem of discrete-time Markov jump linear systems (MJLS) with hard constraints on the norm of the state and control variables. Both cases the finite horizon as well as the infinite horizon are considered. Regarding the Markov chain parameter θ(k), it is assumed that the controller only has access to a detector which emits signals θ̂(k) providing information on the parameter θ(k). The goal is to design a static output feedback linear control using the information provided by detector θ̂(k) in order to minimize an upper bound for the quadratic cost and satisfy the hard constraints. For the infinite horizon case it is also imposed that the controller stochastically stabilizes the closed loop system. LMIs (linear matrix inequalities) are formulated in order to obtain a solution for these optimization problems. The cases in which the initial conditions are fixed and when it is desired to maximize an estimate of the domain of an invariant set are also analyzed. Some numerical examples are presented for the purpose of illustrating the results obtained.