This technical note addresses the H ₂ -control problem for a continuous-time Markov Jump Linear System (MJLS) with partial information on the mode of operation. The jumps of the system depend on a continuous-time hidden Markov model (CT-HMM) where the hidden process represents the dynamics of the real system, while the emitted signal represents the information available to the controller. We start by analyzing the stochastic stability control problem with the goal to design a state feedback linear controller that stochastically stabilizes the closed-loop system, relying on the information from the detector. Two dual formulations, based on LMI problems, are derived as a solution for this problem. These results are then extended to the H ₂ guaranteed cost control problem. The technical note is concluded with a numerical example which illustrates the derived results.

This paper deals with the robust H₂-control of discrete-time Markovian jump linear systems. It is assumed that both the state and jump variables are available to the controller. Uncertainties satisfying some norm bounded conditions are considered on the parameters of the system. An upper bound for the H₂-control problem is derived in terms of a linear matrix inequality (LMI) optimization problem. For the case in which there are no uncertainties, we show that the convex formulation is equivalent to the existence of the mean square stabilizing solution for the set of coupled algebraic Riccati equations arising on the quadratic optimal control problem of discrete-time Markovian jump linear systems. Therefore, for the case with no uncertainties, the convex formulation considered in this paper imposes no extra conditions than those in the usual dynamic programming approach. Finally some numerical examples are presented to illustrate the technique.

This letter addresses the H _∞ -control problem for continuous-time Markov jump linear systems where the current mode of operation is estimated by an imperfect detector. Different from existing approaches, the joint jump process is defined in this letter by a continuous-time hidden Markov model, with the hidden process representing the dynamics of the real system while the emitted signal is represented by the information emitted from the detector. We consider static output feedback controllers which depend only on the information emitted from the detector and that stabilize the closed loop system in the mean-square sense. We develop a linear matrix inequality optimization problem which minimizes an upper bound for the H∞ norm of the closed-loop system in order to design our static output feedback controller. This letter is concluded with a numerical example.