Stochastic Sampled Data Control for Hâˆ‍ Stabilization of Transport Reaction Systems

Abstract

This paper investigates the problem of stochastic sampleddata Hâˆ‍ control for a class of parabolic systems governed by onedimensional semilinear transport reaction systems with external disturbances. A sampleddata controller design is developed by introducing the timevarying delay in the control input signals. The m sampling periods are considered whose occurrence probabilities are known constants and satisfy Bernoulli distribution. Since discontinuous Lyapunov functional copes well with problems of sampleddata control systems, a discontinuous Lyapunov functional is constructed based on the extended Wirtinger’s inequality. With this new approach, sufficient conditions that guarantee the asymptotic meansquare stabilization of the considered systems and the L2gain analysis are derived in terms of linear matrix inequalities (LMIs), which can be solved by any of the available software.