Showing papers by "Ian R. Petersen published in 1990"
TL;DR: In this paper, the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time-domain results on the quadratic stabilization of uncertain systems and the frequency domain results on H/sup infinity / optimization.
Abstract: The problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time-domain results on the quadratic stabilization of uncertain systems and the frequency-domain results on H/sup infinity / optimization. A complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given. Relations between these robust stabilization problems and H/sup infinity / control theory are explored. It is also shown that in a number of cases, if a robust stabilization problem can be solved via Lyapunov methods, then it can be also be solved via H/sup infinity / control theory-based methods. >
1,464 citations
TL;DR: In this article, an extension to a well-known theorem due to Kharitonov is presented, which gives a necessary and sufficient condition for all polynomials in a given family to be Hurwitz stable.
Abstract: An extension to a well-known theorem due to Kharitonov is presented, Kharitonov's theorem gives a necessary and sufficient condition for all polynomials in a given family to be Hurwitz stable. In Kharitonov's theorem, the family of polynomials considered is obtained by allowing each of the polynomial coefficients to vary independently within an interval. Kharitonov's theorem shows that stability of this family of polynomials can be determined by looking at the stability of four specially constructed vertex polynomials. Kharitonov's theorem is extended to allow for more general families of polynomials and to allow a given margin of stability to be guaranteed for the family of polynomials. >
32 citations
01 Jan 1990
TL;DR: In this paper, the authors considered a class of linear uncertain systems and showed that if the uncertain system satisfies a certain matching condition then the system will be feedback controllable, and this matching condition is also known to be a sufficient condition for the stabilizability of the system.
Abstract: This paper considers a problem of controllability for a class of linear uncertain systems. The uncertain systems under consideration contain norm bounded time-varying uncertainty. The paper introduces a new notion of controllability referred to as feedback controllability. Roughly speaking, an uncertain system is feedback controllable if there exists a time varying linear state feedback control such that with any initial condition, the closed loop system state converges to zero in a finite time. The main result of the paper shows that if the uncertain system satisfies a certain matching condition then the system will be feedback controllable. This matching condition is also known to be a sufficient condition for the stabilizability of the uncertain system.
7 citations
TL;DR: In this article, the problem of determining the stabilizability of a linear system with uncertain parameters contained in the system matrix is considered and equivalence relations between the two approaches are determined for both single and multiple rank-one uncertainty.
3 citations
05 Dec 1990
TL;DR: In this paper, the efficacy of nonlinear control in the quadratic stabilization of linear systems containing norm bounded uncertainty is considered and the main result of this conjecture is proved for a class of uncertain systems containing a single scalar uncertain parameter.
Abstract: The efficacy of nonlinear control in the quadratic stabilization of linear systems containing norm bounded uncertainty is considered. In particular, the author examines the quadratic stabilization of uncertain systems via dynamic output feedback control. It is conjectured that, if a linear system containing norm bounded uncertainty can be stabilized via nonlinear control, then it can also be stabilized using linear control. The main result of this work proves this conjecture for a class of uncertain systems containing a single scalar uncertain parameter. >
2 citations