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Chapter 4
Stable Fuzzy Control System by Design
José Manuel Andújar, Antonio Javier Barragán, Basil Mohammed
Al-Hadithi, Fernando Matía and Agustín Jiménez
4.1 Introduction
The control problem is closely linked to the concept of stability. So much so these
concepts are linked, it makes no sense to talk about control systems if these are
not stable. When it is desired to design a control system for a nonlinear plant is
desirable, and sometimes necessary, do not use linear approximations; since the loss
of information that this implies, may cause the resulting system not be stable, or be
very locally.
Nonlinear systems have a great wealth in their dynamic responses (Isidori
1999
;
Khalil
2000
; Marquez
2003
; Sastry
1999
; Slotine and Li
1991
). This richness makes
it very difficult to achieve a theory that allows the design of control systems in a
systematic way, as with linear systems. However, as long as the mathematical model
of the plant is known, there are many control techniques that can be applied to the
synthesis of nonlinear controllers, such as feedback linearization, gain scheduling,
adaptive control or sliding control, among others. Given the inherent ability of the
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