Stability analysis of digital feedback control systems with time-varying sampling periods

We consider digital feedback control systems with time-varying sampling period's consisting of an interconnection of a continuous-time nonlinear plant (described by systems of first-order ordinary differential equations), a nonlinear digital controller (described by systems of first-order ordinary difference equations), and appropriate interface elements between the plant and controller (A/D and D/A converters). For such systems we study the stability properties of an equilibrium (in the Lyapunov sense) and derive some results for local stability and instability via a linearization approach. These results are then used in the analysis of certain classes of switched systems and in the stabilization problem of nonlinear cascade control systems via hybrid feedback controllers. (C) 2000 Elsevier Science Ltd. All rights reserved.