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

Abstract

This paper presents an indirect adaptive stabilization scheme forfirst-order continuous-time systems under saturated input which isdescribed by a sigmoidal function. The singularities are avoided througha modification scheme for the estimated plant parameter vector so thatits associated Sylvester matrix is guaranteed to be nonsingular andthen the estimated plant model is controllable. The modificationmechanism involves the use of a hysteresis switching function. Analternative hybrid scheme, whose estimated parameters are updated atsampling instants is also given to solve a similar adaptivestabilization problem. Such a scheme also uses hysteresis switching formodification of the parameter estimates so as to ensure thecontrollability of the estimated plant model.