Lyapunov design of stabilizing controllers for cascaded systems
- 1 January 1991
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 36 (10), 1177-1181
- https://doi.org/10.1109/9.90230
Abstract
The design of a state feedback law for an affine nonlinear system to render a (as small as possible) compact neighborhood of the equilibrium of interest globally attractive is discussed. Following Z. Artstein's theorem (1983), the problem can be solved by designing a so-called control Lyapunov function. For systems which are in a cascade form, a Lyapunov function meeting Artstein's conditions is designed, assuming the knowledge of a control law stabilizing the equilibrium of the head nonlinear subsystem. In particular, for planar systems, this gives sufficient and necessary conditions for a compact neighborhood of the equilibrium to be stabilized.Keywords
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