Stability of a Class of Discrete Time Systems with a Single Feedback Nonlinearity.

摘要

In this report, the new Lyapunov function introduced recently by the authors is used in order to derive sufficient conditions for the absolute stability of the sampled-data control system which is composed of a linear time-invariant plant characterized by the transfer function in the forward path and a nonlinear feedback element whose argument is a linear combination of the system state variables. The main contribution of this report is the derivation of frequency domain stability criteria for the linear plant in the case of continuous monotone increasing and odd monotone increasing nonlinear feedback functions which have a continuous and bounded derivative and satisfy certain inequality statements. These frequency domain stability criteria provide a direct, systematic method for the generation of explicit Lyapunov functions. In addition, for the case of certain nonlinear time-varying feedback elements, the Lyapunov function is employed to derive a geometrical method, completely analogous to the Circle Criterion of continuous-time dynamical systems, for determining the range of absolute stability of the sampled-data control system through the examination of the frequency response of the time-invariant plant. (Author)