Stability analysis and state-feedback control of LPV systems with piecewise constant parameters subject to spontaneous Poissonian jumps

摘要

LPV systems with piecewise constant parameters subject to spontaneousPoissonian jumps are a class of systems that does not seem to have beenthoroughly considered in the literature. We partially fill this gap here byproviding sufficient stability and performance analysis conditions stated interms of infinite-dimensional LMI problems that can be solved using sum ofsquares programming. A particularity of the obtained conditions lies in thepresence of an integral term leading to some technical difficulties whenattempting to obtain convex conditions for the design of a gain-scheduledstate-feedback controller. This difficulty is circumvented by relying on arecent result for time-delay systems analysis and an equivalent integral-freeLMI condition is obtained. The approach is illustrated through severalexamples.