Stability analysis and state-feedback control of LPV systems with piecewise constant parameters subject to spontaneous Poissonian jumps
It fills a gap in the literature for a specific class of LPV systems, but the contribution is incremental as it extends existing techniques.
This paper addresses stability analysis and state-feedback control for LPV systems with piecewise constant parameters subject to spontaneous Poissonian jumps, providing sufficient conditions via infinite-dimensional LMIs solved with sum-of-squares programming. The method is illustrated with examples.
LPV systems with piecewise constant parameters subject to spontaneous Poissonian jumps are a class of systems that does not seem to have been thoroughly considered in the literature. We partially fill this gap here by providing sufficient stability and performance analysis conditions stated in terms of infinite-dimensional LMI problems that can be solved using sum of squares programming. A particularity of the obtained conditions lies in the presence of an integral term leading to some technical difficulties when attempting to obtain convex conditions for the design of a gain-scheduled state-feedback controller. This difficulty is circumvented by relying on a recent result for time-delay systems analysis and an equivalent integral-free LMI condition is obtained. The approach is illustrated through several examples.