Ultimate Boundedness and Asymptotic Stability of Uncertain Dynamical Systems Via Variable Structure Control Approach

This paper is devoted to feedback control of a class of imperfectly known dynamical systems. State feedback structures are proposed which guarantee uniform ultimate boundedness (practical stability) of all motions of the closed-loop system. A transformation which decouples the "fast" and "slow" states is utilized in the analysis. A variable structure control approach and Lyapunov type arguments are employed to find the ultimate bounds for a subclass of closed-loop uncertain systems with matched and unmatched bounded uncertainties.