A new definition of dissipativity and its applications

Traditional definitions of dissipativity require an assumption that the admissible control should guarantee that the system has a unique solution and the supply rate is locally integrable. In this paper, by introducing the first exit time from a changeable domain of state and input, a novel dissipativity in the local form and the global sense is defined based on some easily-checked conditions. By the aid of the new definition, a criterion on existence of solution (which will be used before stability analysis) is proposed. All our efforts are to construct a new framework of dissipative-system theory which includes some standard results in traditional dissipative theory and Lyapunov methods as special cases. Therefore, the theoretic analysis is more rigorous and the range of applications is greatly broadened.