Piecewsie quadratic stability for piecewise linear differential inclusions
Raffaele Iervolino, University of Napoli Federico II, Italy
Piecewise linear systems represent a class of hybrid systems characterized by a partition of the state-space into regions where system dynamics can be described by linear models. Unfortunately, mathematical models of practical systems are always affected by uncertainties of various kind. We consider uncertain autonomous piecewise linear systems where the state partition consists of convex polyhedral cones and in each cone the uncertain dynamic matrix can be expressed as a convex hull of known matrices. Such class of systems can be viewed as piecewise linear differential inclusions. Among others, examples of nonlinear systems which can be embedded in this framework are Lur’e systems with possibly asymmetric domain of the feedback characteristic and power electronics converters.
We tackle the absolute stability issue for of piecewise linear differential inclusions by using a cone-copositive approach. The stability problem is formulated as a set of linear matrix inequalities each constrained into a specific cone, i.e. a set of cone-copositive programming problems. A procedure for solving the set of constrained inequalities is under study. The proposed approach allows less conservative estimation of the robust stability region with respect to the classical Circle criterion and to other approaches based on piecewise quadratic Lyapunov function.
Laurea Magistralis Theses
R. Iervolino, L. Iannelli, F. Vasca, "A Cone-copositive Approach for the Stability of Piecewise Linear Di.erential Inclusions", 50th IEEE Conference on Decision and Control, Orlando, FL, USA, December 2011, p. 1062-1067.
F. Vasca, R. Iervolino, L. Iannelli, "Stability of Lur'e Systems with Piecewise Linear Sector Bounds", 19th Mediterranean Conference on Control and Automation, Corfu, Greece, June 2011, p. 1337-1342.
R. Iervolino, L. Iannelli, F. Vasca, "Absolute Stability of Lur'e Systems: a Complementarity and Passivity Approach", 49th IEEE Conference on Decision and Control, Atlanta, Georgia, December 2010, p. 2420-2425.