Equilibria of recurrent fuzzy systems (Q1414803)

The paper is concerned with fuzzy control systems in two directions: modelling and qualitative behavior of equilibria. The modelling part shows how recurrent fuzzy systems can be modelled by the usual control recurrence \[ x_{k+1} = f(x_k,u_k) \] and establishes some basic properties of \(f\). Further, the existence of at least one equilibrium for any constant input \(u\) is proved; since \(f\) is globally Lipschitz with the Lipschitz constant \(1\) (non-expansiveness), the authors easily prove Lyapunov stability of any equilibrium. It is also shown that chaotic motions are excluded for such systems.