Summary: Guaranteed­Cost Control of the Nonlinear Benchmark
Problem Using Model­Based Fuzzy Systems
Ali Jadbabaie, Chaouki T. Abdallah, Mohammad Jamshidi, and Peter Dorato
Department of Electrical and Computer Engineering
University of New Mexico
Albuquerque, NM 87131, USA
falij, chaouki, jamshidig@eece.unm.edu
SUBMITTED TO THE 1998 CCA CONFERENCE
Abstract
In this paper we design a state­feedback controller for the nonlinear benchmark problem.
Our approach relies on the use of Takagi­Sugeno fuzzy models to approximate the nonlinear
system. Once the fuzzy model is obtained, we develop a guaranteed­cost framework to design
the controller using Linear Matrix Inequality methods and recently obtained relaxed stability
conditions. We show that our proposed controller will not only stabilize the system, but also
has satisfactory disturbance attenuation properties.
1 Introduction
The nonlinear benchmark problem was introduced in [18] as a simplified model of a dual­spin
spacecraft to study the resonance capture phenomenon [12]. It has since been clarified and
proposed as a benchmark to study nonlinear control techniques [3]. After simplification, the
system is described by the non­dimensional equations

Source: Abdallah, Chaouki T- Electrical and Computer Engineering Department, University of New Mexico

Collections: Engineering