Dissipativity-based backstepping boundary control for a class of semilinear partial integro-differential equations

Abstract

Abstract The problem of state feedback control for a class of semilinear partial integro-differential equations is addressed within the framework of dissipativity theory. Adapting ideas from absolute stability theory the system is viewed as interconnection of a linear dynamic and a nonlinear static subsystem. Using this interpretation sufficient conditions for the stabilization of the zero solution by means of a backstepping state feedback controller are derived considering a class of nonlinearities satisfying a quadratic dissipativity condition. The approach is illustrated using numerical simulations for a representative case example.