Posted Dec 1, 1995
This paper concerns a general dissipative control problem for nonlinear systems with full state feedback. This problem includes positive real control and H control problems as special cases. The paper shows that the solution to the control problem is equivalent to the existence of a type of solution to a partial differential inequality (nonlinear systems case) or an algebraic Riccati inequality (linear systems case) and stability results are obtained under appropriate detectability assumptions. That is the main pursuit of the paper. In addition, we obtain a local smooth solution to the PDI based on the solution for the linearized systems. Finally, we consider an application of the results to a robust stabilization problem.