Improved LMI conditions for gain scheduling and related control problems

✍ Scribed by Gérard Scorletti; Laurent El Ghaoui

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 240 KB
• Volume: 8
• Category: Article
• ISSN: 1049-8923
• DOI: 10.1002/(sici)1099-1239(199808)8:10<845::aid-rnc350>3.0.co;2-i

✦ Synopsis

The gain scheduling problem considered in this paper concerns a linear system whose state-space equations depend rationally on real, time-varying parameters, which are measured in real time. A stabilizing, parameter-dependent controller is sought, such that a given L -gain bound for the closed-loop system is ensured. Sufficient linear matrix inequality (LMI) conditions are known, that guarantee the existence of such 'gain-scheduled' controllers.

This paper improves these results in two directions. First, we show how to exploit the realness of the parameters using a 'skew-symmetric scaling' technique. Moreover, we show how to apply this technique in a time-varying and/or nonlinear setting.

We first devise a general result pertaining to control synthesis of interconnection of dissipative operators, and apply it to the gain-scheduling problem. Owing to its generality, this result can be applied to other problems such as anti-windup control, nonlinear control and model reduction.