$\mathcal {H}_{\infty }$ Control of Constrained Markov Jump Systems With Intermittent Mode Information Loss

Abstract

This paper investigates <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> control for continuous-time Markov jump systems subject to joint input-state constraint and intermittent mode information loss. The considered constraint, which is defined as a quadratic function of the system state and control input, is very general since it covers the input constraint, state constraint or other constraints for physical quantities of interest. The mode information loss is described by a Bernoulli stochastic process. As a result, the system mode and controller mode form a special case of hidden Markov model. By means of an mode-dependent Lyapunov function, a sufficient condition is presented which can guarantee that the closed-loop system is exponentially mean square stable with a certain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> noise attenuation performance under the joint input-state constraint. Finally, an example is presented to analyze the influence of some important parameters and illustrate the effectiveness of the proposed control scheme.