Structural stability of linear dynamically varying (LDV) controllers

LDV systems are linear systems with parameters varying according to a nonli near dynamical system. This paper examines the robust stability of such sys tems in the face of perturbations of the nonlinear system. Three classes of perturbations are examined: differentiable functions, Lipschitz continuous functions and continuous functions. It is found that in the first two case s the system remains stable. Whereas, if the perturbations are among contin uous functions, the closed-loop may not be asymptotically stable, but, inst ead, is asymptotically bounded with the diameter of the residual set bounde d by a function that is continuous in the size of the perturbation. It is a lso shown that in the case of differential perturbations, the resulting opt imal LDV controller is continuous in the size of the perturbation. An examp le is presented that illustrates the continuity of the variation of the con troller in the case of a nonstructurally stable dynamical system. (C) 2001 Elsevier Science B.V. All rights reserved.