Simultaneous stabilization of LTI systems by means of nonlinear time-varying feedback

Ho-Mock-Qai, Bertina

doi:10.1109/acc.1997.612039

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Proof Of Theorem 321

Robust Stabilization When the Sign Of B á Is Constant On G1

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Cited by 8 publications

(3 citation statements)

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“…It is easily seen [7,Lemma C2,p. 167] that the sets W À b and W b become smaller and smaller as b tends to 0.…”

Section: Proof Of Theorem 32mentioning

confidence: 97%

“…On the other hand, u k 0 depends on a partition of unity which might be di½cult to express. It turns out that the mappings of this partition of unity can be substituted for by simple and explicit mappings (which nevertheless yield less insight into the construction) in order to get an explicit robust asymptotic stabilizer (see [7] for further details).…”

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

confidence: 99%

“…. ; d, are real analytic on some neighborhood of the origin in R 2 (see Lemma A.5 on p. 148 of [7] for further details). Next, because q f g x 1 ; x 2 =qx 1 j 0; 0 0 0, we obtain that d 1, and the lemma follows.…”

mentioning

confidence: 99%

See 2 more Smart Citations

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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“…It is easily seen [7,Lemma C2,p. 167] that the sets W À b and W b become smaller and smaller as b tends to 0.…”

Section: Proof Of Theorem 32mentioning

confidence: 97%

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

confidence: 99%