Estimation of the practical stability region of a class of robust controllers with input constraint

Peng, Shou-Tao; Chen, Cha’o-Kuang

doi:10.1016/s0016-0032(97)00072-0

Cited by 4 publications

(6 citation statements)

References 12 publications

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“…Research on partial stability (stabilization) and control also covers -problems in celestial mechanics [37,38,138,227], -convergence of certain optimization algorithms [94], -abstract nonlinear Cauchy problems [154], -stability of a proper vortex n-gon [69], -coordinate synchronization of dynamic systems [327,199,14,15,30,200] related with safe communication (in synchronization of chaotic systems), -estimation of states and domain of partial stability of dynamic systems [16,269], -stability of radar systems [150], -computer network traffic balancing [252], and -stability of biotechnical processes [271]. Let us consider examples on the partial stability of the zero equilibrium position of a holonomic Lagrangian system, partial stabilization of the permanent rotation of an asymmetric solid with a flywheel, and partial control of the angular motion of a solid.…”

Section: Applications and Examplesmentioning

confidence: 99%

Partial stability and control: The state-of-the-art and development prospects

Vorotnikov¹

2005

Autom Remote Control

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Problems in bordering fields associated with partial stability and stabilization of nonlinear dynamic systems, including partial stability and stabilization by part of coordinates of the phase vector, are reviewed. They are classified, and their relation with other stability and stabilization problems, including recent ones, are considered. Main development trends in theory and research methods are surveyed and certain results and applications are described. The partial control notion in border disciplines is examined. A long list of references is given.

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Section: Applications and Examplesmentioning

confidence: 99%

Partial stability and control: The state-of-the-art and development prospects

Vorotnikov¹

2005

Autom Remote Control

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“…By the de"nition of C, (C G (t, x))) G , and so any selection from C is bounded. Although the generalized state-feedback (14) satis"es the control constraints, it is not clear that this saturation-type controller will &stabilize' system (2). However, it is shown in the ensuing analysis that, under a feasibility hypothesis (stated in H3 below), stability can be achieved.…”

Section: Constrained Controls and System Stabilizationmentioning

confidence: 99%

“…Suppose hypotheses H1}H4 hold and "0. The class of uncertain systems modelled by (2) is globally uniformly practically stable if 0( (1, with bounded generalized state-feedback control u"C(t, x), de"ned in (14).…”

Section: Theorem 52mentioning

confidence: 99%

“…Suppose hypotheses H1}H2 and H4 hold, "0, and "0. If (1, then, under the dynamics of system (2) with feedback control (14), +0, is globally uniformly asymptotically stable.…”

Section: Corollary 52mentioning

confidence: 99%

“…Suppose hypotheses H1}H5 hold and *1. Then, with bounded generalized state-feedback u"C(t, x), speci"ed in (14) with * '0 and ( ( , any sub-level set V(rL ), such that…”

Section: Lemma 51mentioning

confidence: 99%

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Stabilization of a class of uncertain nonlinear affine systems subject to control constraints

Goodall

Wang

2001

Intl J Robust & Nonlinear

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SUMMARYPractical and asymptotic stabilization is investigated for a class of uncertain nonlinear a$ne control systems subject to constraints on the control inputs. The uncertain systems are modelled as non-linear perturbations to a known non-linear idealized system and a problem formulation based on di!erential inclusions is adopted. A class of constrained generalized state-feedback controls (containing both continuous and discontinuous selections) is developed, which guarantees stabilization with a speci"ed region of attraction. In the presence of residual uncertainty, su$cient conditions for global stabilizability are presented, whilst local results are obtained by relaxing these conditions.

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