Feedback linearization, stability and control of piecewise affine systems exploiting canonical and conventional representations

Piecewise Affine (PWA) systems constitute a quantitatively simple yet qualitatively rich subclass of nonlinear systems. On the one hand, two-segment PWA ideal diode model, which is the most basic nonlinear circuit element of electrical engineering, can be considered as the simplest example. On the other hand, Chua?s circuit, which demonstrates one of the most complicated nonlinear dynamical behaviors, i.e. chaos, contains a three-segment PWA resistor as the unique nonlinear element. PWA system and controller models are becoming attractive in control area since they allow exploiting linear analysis techniques and providing a suitable structure for which the extension of the control system analysis and design methods originally developed for linear systems into this special nonlinear system class is possible. The thesis has three main contributions to the PWA control systems area. For the PWA control systems, the thesis introduces the development of feedback linearization methods for PWA control systems based on the canonical representation. The second contribution is the proposed robust chaotification method by sliding mode control. For the stability analysis of PWA control systems, a novel quadratic Lyapunov function based on intersection of degenerate ellipsoids and vertex representations of the polyhedral regions is the third contribution of the thesis. The absolute value based canonical representation employed in feedback linearization of PWA control systems provides parameterizations and compact closed form solutions for the controller design by feedback linearization. These parameterizations and closed form solutions constitute a basis for further theoretical and applied studies on the analysis and design of control systems. Keywords : Piecewise affine, Lyapunov stability, feedback linearization, chaotification, sliding mode control