Abstract: 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.