Stabilization of Nonnecessarily Inversely Stable First-Order Adaptive Systems under Saturated Input

This paper presents an indirect adaptive stabilization scheme for first-order continuous-time systems under saturated input which is described by a sigmoidal function. The singularities are avoided through a modification scheme for the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be non-singular and then the estimated plant model is controllable. The modification mechanism involves the use of a hysteresis switching function. An alternative hybrid scheme, whose estimated parameters are updated at sampling instants is also given to solve a similar adaptive stabilization problem. Such a scheme also uses hysteresis switching for modification of the parameter estimates so as to ensure the controllability of the estimated plant model.

Authors:

• M. De la Sen
• O. Barambones

Keywords:

• Hybrid dynamic systems
• discrete systems
• saturated input
• control
• stabilization.

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