Recurrent Dissipativity-Based Inequalities for Controller Design

Using a new set of semidefinite constraints called recurrent dissipativity-based inequalities (DBIs), this letter presents an iterative procedure to design polynomial feedback control laws for polynomial nonlinear systems, let it be a static state feedback or a linear static output feedback (SOF) controller one needs to determine. In addition to that, the problem of linear SOF design for linear time-invariant (LTI) systems is solved as well. In the case of polynomial systems, we use sum-of-squares (SOS) programming for controller design and to provide an estimate of the closed-loop domain of attraction. In the case of LTI models, a set of linear matrix inequalities (LMIs) is employed in an iterative strategy to determine a stabilizing gain. Numerical simulations on a few examples borrowed from literature are provided in order to emphasize the advantages of our new dissipativity-based control (DBC) method.