Algebraic Approach for Modelling and Analysis of Nonlinear Hybrid Dynamical Systems

This work is concerned with hybrid dynamical systems and their stability analysis using on the one hand the direct Lyapunov method and the advantages of the tensor notation for nonlinear systems on the other hand. In order to provide the systematic formulation of the stability conditions as LMI tests a corresponding approach is proposed. This approach is based on the use of the Kronecker product mathematical tool which leads to the description of the analytic vector fields by polynomial functions and allows various algebraic manipulations.