Multi-valued control of port-Hamiltonian systems

We consider the use of multi-valued control laws for port-Hamiltonian systems. It is shown that if the multi-valued controller is monotonically increasing, then the control action is passive, the closed-loop system is well-defined, and robust output regulation is achieved. We propose a concrete methodology to construct maximal monotonically increasing controls. The scheme can be naturally applied to systems originally described by multi-valued operators, such as mechanical systems with unilateral constraints and circuits with diodes and transistors.