Foundations of Feedback Theory for Nonlinear Dynamical Systems

S---We study the fundamental properties of feedback for nonlinear, ~ time-varying, multi-input, multi-output,distributed systems. The classical Black formula is generalized to the nonlinear case. Achievable advantages and limitations of feedback in nonlinear dynamical systems 1are classified and rtudied in five, categories: desensitization, C disturbance attenuation, linearizing effect, asymptotic tracking and disturbance rejection, stabilization. Conditions under which feedback is beneficial for nonlinear dynamical systems are derived. Our results show that if the appropriate linearized inverse return difference operator is small, then the nonlinear feedback system has advantages over the open-loop system. Several examples are provided to illustrate the results. Research sponsored by the National Science Foundari nGr. 2 0 and the Joint Services Electronics Progrw J j 620-76-C-__/N-.I"Z ' _17 _ _ S~EE i LT: i6;i / <, 1