On the stability of motion

The following system considered in this paper:This system is referred to as a half-linear system. The coefficient f (t) is assumed to be bounded, but the coefficients e(t), g(t) and h(t) are not necessarily bounded. Sufficient conditions are obtained for global asymptotic stability of the zero solution.Our results can be applied to not only the case that the signs of f (t) and g(t) change like the periodic function but also the case that f (t) and g(t) irregularly have zeros.Some suitable examples are included to illustrate our results.

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“…Matrosov's theorem was extended in various directions by himself and many researchers (for example, see [3,21,22,33,37,[45][46][47]49,50]). …”

Section: Theorem 32 Let Assumptions ( a 1 ) And (A 2 ) Hold And Suppmentioning

confidence: 99%

Global asymptotic stability for half-linear differential systems with generalized almost periodic coefficients

Sugie

Hata

2011

Monatsh Math

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“…For an arbitrary control input, an explicit function of time, we resort to one of the techniques called "invariance-like" methods by Khalil [21]. In particular, we use the theorem first presented by Matrosov [22] and extended to non-scalar auxiliary functions by Rouche [23]. We refer readers to the translated Matrosov paper and the Rouche paper for proofs of the original theorems.…”

Section: A Stability Analysismentioning

confidence: 99%

“…Theorem IV.1 (Rouche Theorem 4.4 from [23]: sufficient conditions for uniform asymptotic stability). Let there exist two functions V (t, x) : R × B ρ → R and W (t, x) :…”

Section: A Stability Analysismentioning

confidence: 99%

An almost global estimator on SO(3) with measurement on S<sup>2</sup>

Swensen

Cowan

2012

2012 American Control Conference (ACC)

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Abstract-This paper presents an almost globally convergent state estimator for the orientation of a rotating rigid body. The estimator requires knowledge of the angular velocity of the body at each time instant and the measurement consists of a single unit vector on the body, which we take without loss of generality to be the first column of the rotation matrix. The stability proof involves a relatively simple Lyapunov and invariance-like analysis. A mild non-degeneracy constraint on the control input guarantees the fulfillment of the invariance criterion. We apply the result to needle-tip orientation estimation for tip-steerable needles.

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Théorie de la stabilité dans les équations difféerentielles ordinaires

Rouche

2010

Stability Problems

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On the stability of motion

Cited by 13 publications

References 2 publications

Global asymptotic stability for half-linear differential systems with generalized almost periodic coefficients

Global asymptotic stability for half-linear differential systems with generalized almost periodic coefficients

An almost global estimator on SO(3) with measurement on S<sup>2</sup>

Théorie de la stabilité dans les équations difféerentielles ordinaires

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