Showing papers by "Ian R. Petersen published in 1988"
TL;DR: In this paper, the authors considered a H/sub infinity /-optimal control problem in which the measured outputs are the states of the plant and showed that the infimum of the norm of the closed-loop transfer function using linear static state-feedback equals the √ √ n −1/n −1 √ 2/n √ 1/n/n−2 √ 0.
Abstract: A H/sub infinity /-optimal control problem in which the measured outputs are the states of the plant is considered. The main result shows that the infimum of the norm of the closed-loop transfer function using linear static state-feedback equals the infimum of the norm of the closed-loop transfer function over all stabilizing dynamic (even, nonlinear time-varying) state-feedback controllers. >
220 citations
TL;DR: In this paper, the authors present a procedure for stabilizing a class of uncertain linear systems by repeated solution of an algebraic Riccati equation, which is then used to construct a stabilizing linear control law.
Abstract: This paper presents a procedure for stabilizing a class of uncertain linear systems. The uncertain systems under consideration are described by state equations in which the input matrix depends on a matrix of uncertain parameters. This matrix of uncertain parameters may be time-varying; however, it is constrained by a bound on its induced norm.The stabilization procedure presented involves the repeated solution of an algebraic Riccati equation. When a positive definite solution to this Riccati equation is obtained, this solution is used to construct a stabilizing linear control law. Another important result contained in this paper can be stated roughly as follows: For the class of uncertain systems under consideration, if a system can be stabilized via nonlinear control, then it is also possible to stabilize the system via linear control.
78 citations
TL;DR: In this article, it was shown that if a certain minimum phase condition is satisfied, then the transfer function bound achievable using state feedback can be asymptotically recovered using a high gain observer.
Abstract: In recent years, a number of approaches have been developed for solving the following problem in linear systems theory: design a state feedback control so that the norm of a specified transfer function is less than a given bound over all frequencies. This paper deals with the case in which not all systems states can be measured. It shows that if a certain minimum phase condition is satisfied, then the transfer function bound achievable using state feedback can be asymptotically recovered using a high gain observer. These results have application to the problems of disturbance attenuation, H∞ optimization and the stabilization of uncertain linear systems.
50 citations
TL;DR: In this article, the problem of stabilizing an uncertain linear system using state feedback control is addressed, where the uncertain parameters are classified into two types: either constant or time-varying.
Abstract: This paper is concerned with the problem of stabilizing an uncertain linear system using state feedback control. The uncertain systems under consideration are described by state equations containing unknown but bounded uncertain parameters. The uncertain parameters are classified into two types: either constant or time-varying. Indeed, the main feature of this paper is that it allows one to exploit the fact that some of the uncertain parameters are constant. In order to investigate the question of stabilizability, quadratic Lyapunov functions are used. Hence, the paper deals with the notion of quadratic stabilizability. The main result of the paper is a necessary and sufficient condition for the quadratic stabilizability of the uncertain systems under consideration.
46 citations
TL;DR: In this article, the Riccati equations arising in linear quadratic differential games were studied and it was shown that if a certain minimum phase condition is satisfied, then the corresponding solution to the corresponding equation will also approach zero.
38 citations
15 Jun 1988
TL;DR: In this paper, it was shown that if a certain minimum phase condition is satisfied then the transfer function bound achievable using state feedback can be asymptotically recovered using a high gain observer.
Abstract: In recent years, a number of approaches have been developed for solving the following problem in linear systems theory: Design a state feedback control so that the norm of a specified transfer function is less than a given bound over all frequencies. This paper deals with the case in which not all system states can be measured. It shows that if a certain minimum phase condition is satisfied then the transfer function bound achievable using state feedback can be asymptotically recovered using a high gain observer.
21 citations
TL;DR: In this article, a high-gain observer is used to recover the disturbance attenuation properties asymptotically, which can be achieved using full state feedback, and then the problems of disturbance via state feedback can then be solved using existing methods based on the algebraic Riccati equation.
Abstract: A procedure is developed for disturbance attenuation in a linear system via the use of measurement feedback. A high-gain observer is used to recover the disturbance attenuation properties asymptotically, which can be achieved using full state feedback. It is thus shown that the problem of disturbance attenuation via measurement feedback can be decomposed into two problems of disturbance attenuation via state feedback. These problems of disturbance via state feedback can then be solved using existing methods based on the algebraic Riccati equation.
15 citations
07 Dec 1988
TL;DR: In this article, the authors considered a problem of disturbance attenuation using full state feedback and gave a complete solution to this problem in terms of a certain algebraic Riccati equation.
Abstract: The author considers a problem of disturbance attenuation using full state feedback. The particular class of linear systems under state feedback is closely related to the so-called one-block problem in H/sup infinity / control. He gives a complete solution to this problem in terms of a certain algebraic Riccati equation. >
6 citations
TL;DR: This note corrects an error in a recent paper on a stabilization algorithm for a class of uncertain linear systems and the result was correct, however, the proof contained an error.
5 citations