On the geometric aspects of the invariant ellipsoid method: Application to the robust control design

This paper deals with a robust control design for a class of nonlinear affine control systems. The dynamical models under consideration are described by ordinary differential equations in the presence of some additive bounded uncertainties. The design procedure for the robust linear feedback control associated with the linearized dynamic model is based on an extended version of the classical invariant ellipsoid method. The stability/robustness analysis of the resulting closed-loop system involves the celebrated Clarke stability theorem that represents a theoretic extension of the celebrated Lyapunov-type methodology. The obtained analytic results are illustrated by a simple computational example.