The peaking phenomenon and the global stabilization of nonlinear systems
- 1 April 1991
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 36 (4) , 424-440
- https://doi.org/10.1109/9.75101
Abstract
The problem of global stabilization is considered for a class of cascade systems. The first part of the cascade is a linear controllable system and the second part is a nonlinear system receiving the inputs from the states of the first part. With zero input, the equilibrium of the nonlinear part is globally asymptotically stable. In linear systems, a peaking phenomenon occurs when high-gain feedback is used to produce eigenvalues with very negative real parts. It is established that the destabilizing effects of peaking can be reduced if the nonlinearities have sufficiently slow growth. A detailed analysis of the peaking phenomenon is provided. The tradeoffs between linear peaking and nonlinear growth conditions are examined.Keywords
This publication has 40 references indexed in Scilit:
- Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systemsIEEE Transactions on Automatic Control, 1991
- Asymptotic stabilization of minimum phase nonlinear systemsIEEE Transactions on Automatic Control, 1991
- Limitations on the stabilizability of globally-minimum-phase systemsIEEE Transactions on Automatic Control, 1990
- Smooth stabilization implies coprime factorizationIEEE Transactions on Automatic Control, 1989
- Adaptive control of linearizable systemsIEEE Transactions on Automatic Control, 1989
- On vanishing stability regions in nonlinear systems with high-gain feedbackIEEE Transactions on Automatic Control, 1986
- A two-stage Lyapunov-Bellman feedback design of a class of nonlinear systemsIEEE Transactions on Automatic Control, 1981
- Output tracking in multivariable nonlinear systemsIEEE Transactions on Automatic Control, 1981
- Bounded peaking in the optimal linear regulator with cheap controlIEEE Transactions on Automatic Control, 1978
- Perturbing uniform asymptotically stable nonlinear systemsJournal of Differential Equations, 1969