Petersen, Ian R.Hollot, Christopher V.2026-06-272026-06-270005-1098ORCID:/0000-0003-4856-9450/work/218729838https://hdl.handle.net/1885/733812161This paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems. The systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set. Furthermore, these uncertain parameters may be time-varying. The method used to establish asymptotic stability of the closed loop system (obtained when the feedback control is applied) involves the use of a quadratic Lyapunov function. The main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic Lyapunov function. Once the Lyapunov function has been obtained, it is used to construct the stabilizing feedback control law. The fundamental idea behind the algorithm presented involves constructing an upper bound for the Lyapunov derivative corresponding to the closed loop system. This upper bound is a quadratic form. By using this upper bounding procedure, a suitable Lyapunov function can be found by solving a certain matrix Riccati equation. Another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic Lyapunov function.*Received 13 May 1985; revised 18 December 1985. The original version of this paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor J. Ackermann under the direction of Editor Dr. Huibert Kwakernaak. A preliminary version of this paper appeared in the IEE Control '85 Conference. This work was supported by the National Science Foundation under grant number ECS-8108804. t Department of Electrical and Electronic Engineering, Australian Defence Force Academy, Campbell, ACT 2600, Australia. :~ Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA01003, U.S.A. Both authors were formerly with the Department of Electrical Engineering, University of Rochester.15en©1986 The authorslinear optimal regulatorLyapunov methodsRiccati equations (non-standard)robustnessstabilitystate feedbackuncertain systems (non-standard)198610.1016/0005-1098(86)90045-20022757589