Global stabilization of partially linear composite systems

A. Saberi, P. V. Kokotovic, H. J. Sussmann

Research output: Contribution to journalConference article

11 Citations (Scopus)

Abstract

It is shown that a linearly controllable and nonlinearly asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if (a) the linear subsystem is right-invertible and weakly minimum phase, and (b) the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output. Both of these conditions are coordinate-free, and there is freedom of choice for the linear output variable. This result generalizes several earlier sufficient conditions for stabilizability. The weak minimum-phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem.

Original languageEnglish (US)
Pages (from-to)1385-1391
Number of pages7
JournalProceedings of the IEEE Conference on Decision and Control
Volume2
StatePublished - Dec 1 1989
EventProceedings of the 28th IEEE Conference on Decision and Control. Part 2 (of 3) - Tampa, FL, USA
Duration: Dec 13 1989Dec 15 1989

Fingerprint

Large scale systems
Subsystem
Stabilization
Composite
State feedback
Output
Stabilizability
Asymptotically Stable
State Feedback
Invertible
Cascade
Linearly
Restriction
Generalise
Sufficient Conditions
Zero

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

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Global stabilization of partially linear composite systems. / Saberi, A.; Kokotovic, P. V.; Sussmann, H. J.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2, 01.12.1989, p. 1385-1391.

Research output: Contribution to journalConference article

TY - JOUR

T1 - Global stabilization of partially linear composite systems

AU - Saberi, A.

AU - Kokotovic, P. V.

AU - Sussmann, H. J.

PY - 1989/12/1

Y1 - 1989/12/1

N2 - It is shown that a linearly controllable and nonlinearly asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if (a) the linear subsystem is right-invertible and weakly minimum phase, and (b) the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output. Both of these conditions are coordinate-free, and there is freedom of choice for the linear output variable. This result generalizes several earlier sufficient conditions for stabilizability. The weak minimum-phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem.

AB - It is shown that a linearly controllable and nonlinearly asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if (a) the linear subsystem is right-invertible and weakly minimum phase, and (b) the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output. Both of these conditions are coordinate-free, and there is freedom of choice for the linear output variable. This result generalizes several earlier sufficient conditions for stabilizability. The weak minimum-phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem.

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