Exponential Hidden Markov Models for <inline-formula> <tex-math notation="LaTeX">${H} _\infty$ </tex-math> </inline-formula> Control of Jumping Systems

Abstract

This letter addresses the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -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.