On optimality of passivity based controllers in discrete-time

The paper deals with connections between optimality and passivity-like properties in discrete time. The problem is set in the framework of differential/difference representations of discrete-time dynamics. The Hamilton–Jacobi–Bellman equality associated with a given cost and the corresponding optimal control solution are characterized. On these bases the connection with uu-average passivity is clarified by exploiting the inverse optimal control problem associated with a given Lyapunov stabilizing feedback. Some constructive cases are analyzed.