Numerical vs Symbolic Computation

This book examines the problem of designing controllers for switched systems that assures stability of the overall system. One method of ensuring the stability is by proving the existence of a Common Lyapunov Function for the system. Most methods involve the formulation of the system dynamic model and constraints into a Linear Matrix Inequality (LMI) structure. Then, computational methods are used to solve the LMI problem. Two problems arise from using LMIs to find solutions. Firstly, available LMI solvers use numerical computation which raises the possibility of rounding off errors. Secondly, the computational burden would be quite heavy. The Haris-Rogers method is an alternative approach that has been developed for designing controllers based on the existence of a Common Lyapunov Function. In this approach, the problem is reduced to solving two sets of Linear Inequalities (LI), hence reducing the computational burden, as compared to methods that use LMIs. To overcome rounding off errors, symbolic computation methods should be used. In this book, a Switched System Control Design Toolbox employing symbolic computation based on the Haris-Rogers solution method was developed.