Stability/Instability Regions for Sampled-Data Control Systems as a function of the Sampling Period and the Plant Obtained from a Liapunov Function

In this work we developed a comparative study between many resolution methods of the exponential matrix from an inequality extracted from a specific Liapunov function to obtain information about some stability regions for sampled-data control systems as a function of the sampling-time and the plant used. We used many methods from the literature like: power series, Cayley-Hamilton theorem, Lagrange-Sylvester theorem, eigenvalues/ eigenvectors decomposition and Padé rational approximation. The main objective of this study is to choose the most appropriate method for the resolution of this important problem and to use the results found as a basis for future works.