On Existence of Periodic Motions in Nonlinear Control Systems with Periodic Inputs
Richard K. Miller, Anthony N. MICHEL · SIAM Journal on Control and Optimization · 1980
The existence of periodic solutions of nonlinear control systems subjected to sinusoidal forcing functions, using the describing function method, is studied. The setting is general enough to allow systems with delays, systems with discontinuous nonlinearities, systems with hysteresis nonlinearities, and so forth. The present results state that if the linearized describing function problem can be solved and if certain bounds (which depend on the exact form of the solution of the describing function problem) can be satisfied, then there is a periodic solution of the exact problem. Furthermore, the present results provide relative error bounds between the response of the exact problem and the associated linearized describing function problem. To demonstrate the applicability of the method advanced, a specific example is considered.