On the practical stability of control processes governed by implicit differential equations: The invariant ellipsoid based approach

This paper deals with a new approach to the robust control design for a class of nonlinearly affine control systems. The dynamical models under consideration are described by implicit differential equations in the presence of additive bounded uncertainties. The proposed robust feedback design procedure is based on an extended version of the classical invariant ellipsoid technique. We call this extension the Attractive Ellipsoid (AE) method. The stability/robustness analysis of the resulting closed-loop system involves a modified descriptor approach associated with the usual Lyapunov-type methodology. The theoretic schemes elaborated in our contribution are finally illustrated by a simple computational example.