Petersen, Ian R.2026-07-032026-07-030167-6911ORCID:/0000-0003-4856-9450/work/219177596https://hdl.handle.net/1885/733812427This paper presents an algorithm for the stabilization of a class of uncertain linear systems. The uncertain systems under consideration are described by state equations which depend on time-varying unknown-but-bounded uncertain parameters. The construction of the stabilizing controller involves solving a certain algebraic Riccati equation. Furthermore, the solution to this Riccati equation defines a quadratic Lyapunov function which is used to establish the stability of the closed-loop system. This leads to a notion of 'quadratic stabilizability'. It is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable. The paper also deals with a notion of 'overbounding' for uncertain linear systems. This procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems. Also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process.7enRiccati equationStabilizationState feedbackUncertain systems198710.1016/0167-6911(87)90102-20023310712