Some generalizations on the ultimate boundedness control of uncertain systems

Abstract

Some generalizations on the ultimate boundedness control of uncertain systems are made in this paper. First, the ‘cone-bounded assumption’ on the plant uncertainties of a class of nominally linear uncertain systems is weakened to a more general ‘K ∞-bounded assumption’. Second, we show that ‘half’ of the uncertain systems with the ‘cone-bounded assumption’ can be practically stabilized via a linear control. Third, for a class of nominally nonlinear uncertain systems with the ‘matching assumption’, a similar smooth nonlinear state feedback control can be constructed to guarantee the uniform ultimate boundedness of the closed-loop trajectories.