On the equivalence between dissipativity and optimality of nonlinear controllers for discontinuous dynamical systems

In this paper, we derive guaranteed gain, sector, and disk margins for nonlinear optimal and inverse optimal discontinuous regulators that minimize a nonlinear-nonquadratic performance functional. Furthermore, we develop a return difference inequality to provide connections between dissipativity and optimality of nonlinear controllers for discontinuous dynamical systems. Specifically, we show that optimal controllers for discontinuous systems satisfy a return difference inequality if and only if the controller is dissipative with respect to a quadratic supply rate map.