Amplitude Dependent Analysis and Stabilization for Nonlinear Sampled-data Control Systems

The robust stability condition for sampled-data control systems with a sector nonlinearity was presented in our previous paper. Although it is applicable only to the sampled-data control system of a certain class, a usual discrete-time control system can belong to this type of class. This paper analyzes the amplitude dependent behavior of nonlinear sampled-data (i.e., discrete-time) control systems in a frequency domain. First, the robust stability condition which was derived in our previous papers is applied to a sampled-data system containing a single time-invariant nonlinear element. Then, an instability condition for that type of nonlinear feedback system is derived. By considering restricted areas (two sectors) in the nonlinear characterisitic, the existence of a sustained oscillation is estimated (whether it is periodic or not), and the relationship between the stable (unstable) conditions and the result which is derived from the classic describing function is compared. Based on these considerations, the stabilization of nonlinear discrete-time control systems is examined in the frequency domain. Copyright ©c 2002 IFAC