Modeling and quadratic stabilization of a class of linear uncertain time‐varying systems

This paper considers the quadratic stabilization of a class of uncertain linear time‐varying (LTV) continuous‐time plants. The state‐space representation of each plant is based on the physically meaningful assumption of a dynamical matrix containing uncertain elements whose time trajectories are sufficiently smooth to be well described by interval polynomial functions with arbitrarily time varying coefficients. At some isolated time instants, the parameters trajectories can exhibit some first‐kind discontinuities due for example to sharply varying operating conditions. Using a parameter independent Lyapunov function, a quadratically stabilizing dynamic output controller is directly obtained by the solution of some LMIs. A salient feature of the paper is that, unlike all the other existing methods, quadratic stabilization can be achieved over possibly arbitrarily large uncertain domains of parameters. Copyright © 2016 John Wiley & Sons, Ltd.