H∞ control for Markovian jump linear singularly perturbed systems

The stochastic stability and H^∞ disturbance attenuation is studied for Markovian jump linear singularly perturbed systems (MJLSPS) via a matrix inequality approach. Both analysis and synthesis problems are investigated. In analysis, the stochastic stability and H^∞ performance conditions are derived and recast in the formulation of a set of coupled linear matrix inequalities. In synthesis, the sufficient conditions under which the closed-loop H^∞ disturbance attenuation performance turn out to be in the form of a set of coupled bilinear matrix inequalities and are solved with a proposed heuristic algorithm, and an ε-independent H^∞ controller can then be obtained. The reduced controller which is independent of the fast states is also developed. The results proposed apply not only to standard, but also to nonstandard MJLSPS. An example is presented to illustrate the proposed algorithm.