Asymptotic Stabilization of a Class of Smooth Two-Dimensional Systems

Dayawansa, W.P.; Martin, Clyde F.; Knowles, Gareth J.

doi:10.1137/0328070

Cited by 132 publications

(26 citation statements)

References 17 publications

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“…The asymptotic stability criteria that we use was ®rst introduced by Dayawansa et al [3], in order to establish the asymptotic stabilizability of a class of twodimensional systems. Here, we use this criteria to prove robust asymptotic stabilizability of families of systems.…”

Section: Robust Stabilization When the Sign Of B á Is Constant On Gmentioning

confidence: 99%

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Nonsmooth Robust Stabilization of a Class of Two-Dimensional Nonlinear Systems

Ho-Mock-Qai¹

1999

Math. Control Signals Systems

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In this paper we consider a class of parameterized families of nonlinear systems which cannot be robustly asymptotically stabilized by means of C 1 feedback. We construct C 0 state feedback laws which are smooth away from the origin and which robustly asymptotically stabilize these families of systems. We then show that, in some cases, the regularity of the obtained robust asymptotic stabilizers is``maximum'' in the sense that the considered families of systems do not admit any Lipschitz continuous robust asymptotic stabilizer.

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Section: Robust Stabilization When the Sign Of B á Is Constant On Gmentioning

confidence: 99%

“…As we shall see later, we manage to construct C 0 robust stabilizers using an asymptotic stability criterion which was introduced in [3].…”

Section: Introductionmentioning

confidence: 99%

Nonsmooth Robust Stabilization of a Class of Two-Dimensional Nonlinear Systems

Ho-Mock-Qai¹

1999

Math. Control Signals Systems

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“…This paper attempts to describe the different dynamical behavior exhibited by (1), in terms of the six parameters, as completely as possible. We hope to gain an analytic insight of this widely used system as much as possible.…”

Section: Introductionmentioning

confidence: 99%

“…Most work in control theory is on stabilisation of nonlinear systems around a fixed point, see e.g. [1] where necessary and sufficient conditions for feedback stabilisation using continuous feedback is given for two-dimensional control systems. Quite recently attention has also been brought to the stabilisation of limit cycles, e.g.…”

Section: Introductionmentioning

confidence: 99%

On the dynamical behaviour of FitzHugh–Nagumo systems: Revisited

Ringkvist

Zhou

2009

Nonlinear Analysis: Theory, Methods & Applications

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“…Thus this type of normal form has been used for the feedback stabilization problem of two dimensional systems. Hamiltonian control systems can not take the form just like (7). Suppose the given system is described in a coordinates (x, y) in R2 as follows: This is due to the results in Section 3.…”

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confidence: 99%