Oscillations in Nonlinear Pulse-modulated Control Systems

Periodical modes in nonlinear control systems with pulse-width and pulse-frequency modulation are considered. The existence of a fixed point for the shift operator along system’s trajectories is frequently used to establish the existence of a periodical mode. However, this method often fails for pulse modulated systems due to discontinuity of the shift operator. The new geometrical approach is proposed for such systems. It is based on construction of convex regions in the state space where the shift operator is continuous. This approach leads to new criteria for the existence of periodical modes that can be easily checked. Consider a nonlinear pulse-modulated system described by the functional-differential equations