Finite-Dimensional H∞Control of a Class of Infinite-Dimensional Linear Time-Varying Systems

✍ Scribed by Hideki Sano

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 237 KB
• Volume: 216
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5698

✦ Synopsis

In this paper, we consider H H control of infinite-dimensional linear time-varying ϱ Ž . IDLTV systems whose homogeneous parts are of modal type, by using a finitedimensional controller. The aim is to construct a finite-dimensional stabilizing controller for the IDLTV system that makes the norm of the closed-loop operator less than a given positive number ␦. To this end, a finite-dimensional model is firstly derived for the IDLTV system, and a stabilizing controller that makes the Ž . norm of the closed-loop operator less than another positive number ␥ -␦ is constructed for the finite-dimensional model. Then it is shown that a controller, which consists of a residual mode filter and the controller mentioned above, becomes a finite-dimensional stabilizing controller for the given IDLTV system such that the closed-loop operator has norm less than ␦ , if the order of the residual mode filter is chosen sufficiently large.