Application of the Simplex Method to the Multi-Variable Stability Problem

In this note, the robust stability problem for nominally linear multi-variable systems with nonlinear, time-varying structured perturbations is considered. To find a better or best Lyapunov function and improve the robust stability bounds, the Simplex method is applied to Lyapunov stablity algorithm. Example of multi-variable case (12×12) is presented to illustrate the proposed analysis.