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IMA Journal of Mathematical Control and Information 1984 1(3):223-242; doi:10.1093/imamci/1.3.223
© 1984 by Institute of Mathematics and its Applications
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Ultimate Boundedness and Asymptotic Stability of a Class of Uncertain Dynamical Systems via Continuous and Discontinuous Feedback Control

E. P. RYAN1 and M. CORLESS2

1School of Mathematics, University of Bath Bath BA2 7AY, England
2Department of Mechanical Engineering, University of California Berkeley, California 94720, USA

Based on concepts from both the theory of variable structure systems and the theory of Leitmann et al., continuous and discontinuous feedback controls are developed which guarantee uniform ultimate boundedness of all motions of a class of imperfectly known dynamical systems with bounded uncertainty. For a subclass of uncertain systems, the zero state can be (a) rendered ‘practically’ stable (in the sense that, given any neighbourhood of the zero state, there exists a control, in the proposed class of continuous feedback controls, which guarantees global uniform ultimate boundedness with respect to that neighbourhood), or (b) rendered globally uniformly asymptotically stable (in the sense of Lyapunov) by the proposed discontinuous feedback control. The approach is illustrated by application to a Maglev suspension control system.


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