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Differential Equation
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Analysis of discretization methods for ordinary differential equations
AN EIGENVALUE CONDITION FOR SAMPLED WEAK CONTROLLABILITY OF BILINEAR SYSTEMS Eduardo
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On exponential stability of nonlinear timevarying differential equations
On exponential stability of nonlinear timevarying differential equations,10.1016/S00051098(99)000126,Automatica,Dirk Aeyels,Joan Peuteman
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On exponential stability of nonlinear timevarying differential equations
(
Citations: 31
)
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Dirk Aeyels
,
Joan Peuteman
Within the Liapunov framework, a sufficient condition for
exponential stability
of ordinary differential equations is proposed. Unlike with classical Liapunov theory, the time derivative of the Liapunov function, taken along solutions of the system, may have positive and negative values. Verification of the conditions of the main theorem may be harder than in the classical case. It is shown that the proposed conditions are useful for the investigation of the
exponential stability
of fast timevarying systems. This sets the stability study by means of averaging in a Liapunov context. In particular, it is established that
exponential stability
of the averaged system implies
exponential stability
of the original fast timevarying system. A comparison of our work with results taken from the literature is included.
Journal:
Automatica
, vol. 35, no. 6, pp. 10911100, 1999
DOI:
10.1016/S00051098(99)000126
Cumulative
Annual
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The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
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www.sciencedirect.com
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Citation Context
(19)
...(see, e.g., [1,
2
, 7, 10, 14, 16]) do not seem welladapted to persistently excited systems, at least for...
Yacine Chitour
,
et al.
On the Stabilization of Persistently Excited Linear Systems
...More refined tools as multiple and nonmonotone Lyapunov functions (see, e.g., [1,
2
, 7, 10, 13, 15]) do not seem welladapted to permanently excited systems, at least for...
Yacine Chitour
,
et al.
On the stabilization of permanently excited linear systems
...Using local charts around p we see now that the conditions of Theorem 3 in [
2
] hold for pair (F;F ) and hence the timevarying systemF (x;t ) is asymptotically stable for sufficiently large . A change of timescales yields asymptotic stability of Cs for the timevarying system (5) for sufficiently small "...
...One can give quantitative estimates for a sufficiently small " based on the averaging theory [
2
]...
Christian Lageman
,
et al.
Synchronization with partial state feedback on SO(n)
...In [
39
], this condition is relaxed and it is shown that if the Lyapunov function decreases when evaluated at a discrete sequence of time instants, the system is asymptotically stable...
...The following Theorem extends the results of [
39
] from the deterministic to the stochastic case and it is used in what follows to establish our main claim...
Maurizio Porfiri
,
et al.
Global stochastic synchronization of chaotic oscillators
...Using recent results on partial averaging tecniques [
33
], [34], wellestablished global synchronization criteria based on Lyapunovstability theory [25], [29], and the concept of matrix measure [35], we establish sufficient conditions for pulse synchronization...
...The proof of our claim combines results from global synchronization of coupled oscillators, based on Lyapunovstability theory [25], [29], with stability results from partial averaging techniques [
33
], [34]...
...In particular, we build on the use of a quadratic Lyapunov function for chaotic systems coupled via a timeinvariant coupling [25], [29] and on the stability results established in [
33
], [34] that are valid for more general Lyapunov functions...
...Nevertheless, global exponential stability of (9a) can be enforced by using the weaker stability conditions presented in [
33
]...
...Indeed Theorem 1 of [
33
], applied to the case at hand, states that if there exists ” > 0 such that for any k 2Z + , V (e((k+1)T))¡V (e(kT)) • ¡”ke(kT)k 2 , where e((k+1)T) is the solution of (9a) with initial condition e(kT) at t = kT , then (9a) is globally exponentially stable...
...In what follows, we show that there exists a finite switching period T ⁄ such that conditions of Theorem 1 of [
33
] apply for any T < T ⁄ . To this aim, we define for every k 2Z +...
...implies that (9a) is globally exponentially stable according to Theorem 1 of [
33
]...
Francesca Fiorilli
,
et al.
Fastswitching pulse synchronization of chaotic oscillators
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Citations
(31)
Averaging techniques without requiring a fast timevarying differential equation
Joan Peuteman
,
Dirk Aeyels
Journal:
Automatica
, vol. 47, no. 1, pp. 192200, 2011
On the Stabilization of Persistently Excited Linear Systems
(
Citations: 1
)
Yacine Chitour
,
Mario Sigalotti
Journal:
Siam Journal on Control and Optimization  SIAM
, vol. 48, no. 6, pp. 40324055, 2010
InputtoState Stability and Averaging of Linear Fast Switching Systems
Wei Wang
,
Dragan Nesic
Journal:
IEEE Transactions on Automatic Control  IEEE TRANS AUTOMAT CONTR
, vol. 55, no. 5, pp. 12741279, 2010
Synchronization with partial state coupling on SO(n)
Alain Sarlette
,
Christian Lageman
Published in 2010.
Global pulse synchronization of chaotic oscillators through fastswitching: theory and experiments
(
Citations: 9
)
Maurizio Porfiri
,
Francesca Fiorilli
Journal:
Chaos Solitons & Fractals  CHAOS SOLITON FRACTAL
, vol. 41, no. 1, pp. 245262, 2009