Robust dissipativity of nonlinear systems with state dependent uncertainties

This paper discusses some conditions under which a nonlinear system with state dependent uncertainties is dissipative with general quadratic supply rate. The uncertainty is described by a nonlinear mapping from the state to an input of the system. The mapping is allowed to be memoryless or to have dynamics in itself. It is shown in this paper that the system is robust dissipative with a C-1 storage function if there exists a scaling function such that Hamilton-Jacobi inequality has a nonnegative solution, and the condition is also necessary under some additional conditions.