On the robust control design for a class of nonlinear affine control systems: The invariant ellipsoid approach

This paper is devoted to the problem of robust design for a class of continuous-time control systems with bounded uncertainties. We study a family of nonlinearly affine dynamical system and apply a modified invariant ellipsoid technique. This makes it possible to obtain practically stable closed-loop controllable models. The design of the stabilizing feedback control strategy is based on the conventional Lyapunov-like approach to invariant sets of dynamical systems. We propose a computational scheme for a constructive treatment a feedback control law such that the region of the practical stability of the resulting system is minimized. The corresponding solution procedure contains an auxiliary LMI-constrained optimization problem. The effectiveness of the elaborated invariant ellipsoid based method is illustrated by a numerical example.