A theorem on global stabilization of nonlinear systems by linear feedback

Tsinias, J.

doi:10.1016/0167-6911(91)90074-o

Cited by 107 publications

(74 citation statements)

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“…Global stabilization of the nonlinear dynamic systems like (1) using the separation principle was considered, for example, in [5,6,14,26,64,89,90,99,104,106,108,130]. The following theorem can be formulated on the basis of the results of [14,139,142,172,173].…”

Section: 3mentioning

confidence: 98%

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Stabilization of Nonlinear Dynamic Systems Using the System State Estimates Made by the Asymptotic Observer

Голубев

Крищенко

Tkachev

2005

Autom Remote Control

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Consideration was given to asymptotic stabilization of the equilibria of nonlinear dynamic systems using the dynamic output feedbacks, that is, the feedbacks in the estimate of system state made by the asymptotic observer. Presented were the basic methods of constructing the asymptotic observers for the nonlinear dynamic systems with control and the approaches to system stabilization using the system state estimate made by the observer.

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Section: 3mentioning

confidence: 98%

“…The dynamic system (1) is regarded as detectable if (i) the weak detectability conditions are met; (ii) d = +∞ and besides the functions α i (·), i = 1, 2, belong to the class K ∞ ; (iii) inequalities (6) and (7) are valid for all x, x ∈ R n , u ∈ R m and all e = x − x ∈ R n .…”

Section: Notation and Definitionsmentioning

confidence: 99%

Stabilization of Nonlinear Dynamic Systems Using the System State Estimates Made by the Asymptotic Observer

Голубев

Крищенко

Tkachev

2005

Autom Remote Control

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“…. ; x n Þ is a positive definite and proper Lyapunov function of the form (12). By simply choosing u ¼ x n nþ1 ; we can verify that ' V n 50; 8x=0 under (10).…”

Section: Proposition 21mentioning

confidence: 98%

A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback

Polendo

Qian

2006

Intl J Robust & Nonlinear

241

170

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SUMMARYIn this paper, we introduce a generalized framework for global output feedback stabilization of a class of uncertain, inherently nonlinear systems of a particularly complex nature since their linearization around the equilibrium is not guaranteed to be either controllable or observable. Based on a new observer/controller construction and a homogeneous domination design, this framework not only unifies the existing output feedback stabilization results, but also leads to more general results which have been never achieved before, establishing this methodology as a universal tool for the global output feedback stabilization of inherently nonlinear systems.

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“…Such popular and fruitful recursive techniques as backstepping and forwarding resulted from these efforts [4,10,11,13,14,18,19,25,26,30,33].…”

Section: Introductionmentioning

confidence: 99%

Global uniform input-to-state stabilization of large-scale interconnections of MIMO generalized triangular form switched systems

Dashkovskiy

Pavlichkov

2012

Math. Control Signals Syst.

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We solve the problem of global uniform input-to-state stabilization with respect to external disturbance signals for a class of large-scale interconnected nonlinear switched systems. The overall system is composed of switched subsystems each of which has the nonlinear MIMO generalized triangular form, which (in contrast to strict-feedback form) has non-invertible input-output maps. The switching signal is an arbitrary unknown piecewise constant function and the feedback constructed does not depend on the switching signal.

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A theorem on global stabilization of nonlinear systems by linear feedback

Cited by 107 publications

References 0 publications

Stabilization of Nonlinear Dynamic Systems Using the System State Estimates Made by the Asymptotic Observer

Stabilization of Nonlinear Dynamic Systems Using the System State Estimates Made by the Asymptotic Observer

A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback

Global uniform input-to-state stabilization of large-scale interconnections of MIMO generalized triangular form switched systems

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