HyStar : A Matlab Toolbox for Robust Regulation of Polytopic Uncertain Piecewise Linear Hybrid Systems

This paper describes a Matlab toolbox for computational analysis and synthesis of a class of piecewise linear hybrid dynamical systems, which are affected by both time varying parametric uncertainties and persistent exterior disturbances. The robust tracking and regulation control problem for such uncertain piecewise linear systems is investigated and solved in two stages. The first stage is to analyze whether there exists an admissible control law such that the closed-loop system exhibits desired behavior. If a specified behavior can be forced on the plant by a control mechanism, then it is called attainable. The method for attainability checking is developed and implemented which employs the predecessor operator and backward reachability analysis. The second stage is to design such admissible control law for a given attainable tracking and regulation specification. The procedure for controller design proposed and implemented here is based on linear programming techniques. A numerical example is used for illustration throughout the paper. ∗The partial support of the National Science Foundation (NSF ECS99-12458 & CCR01-13131) is gratefully acknowledged. The first author appreciates the support from Center of Applied Mathematics Fellowship (2003-04), University of Notre Dame.