Stability criterion and stabilization of linear time-varying systems

A sufficient stability test for linear time-varying systems is proposed by constructing a bounding envelope in which the states of the system are guaranteed to reside. Successive approximations using ellipsoids are performed to build the envelope. The proposed stability assessment method is less conservative than the existing ones and the necessity of point-wise Hurwitz condition is bypassed. The proposed sufficient stability conditions have been transformed into constraints on design parameters to design gain-scheduled controllers which stabilize time-varying systems. Examples are given to validate the effectiveness of the proposed algorithm.