Conservatism reduction in robust control of Markov jump delay systems

A new method is developed for the robust stabilization of a Markov jump system with general discrete state time-delay and partly unknown transition probabilities. In contrast to most existing literature, a set of numerical testable conditions, rather than a huge matrix inequality, are established for the resulting closed-loop system in order to justify the stochastic stability and disturbance attenuation capability with the aid of a non-monotonic design approach. To be specific, by constructing a stochastic Lyapunov function via the application of an n-samples variation, sufficient conditions for the existence of a dissipative state feedback controller are derived with less conservativeness, that is, with larger stochastic stable region and better attenuation level. Three examples including a numerical example, a pest's structured population model and an F-404 test aircraft model are presented to demonstrate the advantage and practical potential of the proposed methodology.