Sontag, E.D.: `Asymptotic amplitudes and Cauchy gains: A small-gain principle and an application to inhibitory biological feedback', Systems and Control Letters, 2002, 47, pp. 167-179. Home/Search Document Not in Database Summary Related Articles Check |
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Some New Directions in Control Theory Inspired by Systems Biology - Sontag (2004) Self-citation (Sontag) (Correct)
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Sontag, E.D.: `Asymptotic amplitudes and Cauchy gains: A small-gain principle and an application to inhibitory biological feedback', Systems and Control Letters, 2002, 47, pp. 167-179.
Crowding Effects Promote Coexistence in the Chemostat - De Leenheer, Angeli, Sontag (2003) Self-citation (Sontag) (Correct)
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E.D. Sontag, Asymptotic amplitudes and Cauchy gains: A small-gain principle and an application to inhibitory biological feedback, Systems Control Lett. 47, 167-179 (2002).
A Small-Gain Theorem for Almost Global Convergence of.. - Angeli, De Leenheer.. Self-citation (Sontag) (Correct)
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Sontag, E.D., "Asymptotic amplitudes and cauchy gains: A small-gain principle and an application to inhibitory biological feedback," Systems and Control Letters 47(2002): 167--179.
Monotone Control Systems - Angeli, Sontag (2002) Self-citation (Sontag) (Correct)
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E.D. Sontag, \Asymptotic amplitudes and Cauchy gains: A small-gain principle and an application to inhibitory biological feedback," Systems and Control Letters, to appear.
On Predator-Prey Systems and Small-Gain Theorems - De Leenheer, Angeli, Sontag (2002) Self-citation (Sontag) (Correct)
....(k x2 k y1 ) u) This result and similar ones following later in the paper, are called small gain theorems. The last condition is often referred to as a small gain condition. We will use this terminology in the sequel. For another example of application of small gain ideas in biology, see [16]) 2.2 Boundedness and stability of Lotka Volterra systems Consider the classical Lotka Volterra system: x = diag(x) Ax r) 18) and r . Note that there are no assumptions on the sign of the entries of A or the components of r. It is possible to show that R is a forward ....
E.D. Sontag, Asymptotic amplitudes and Cauchy gains: A small-gain priciple and an application to inhibitory biological feedback, Systems Control Lett. 47, 167-179 (2002).
A Feedback Perspective for Chemostat Models with Crowding .. - De Leenheer, Angeli.. (2003) Self-citation (Sontag) (Correct)
....in [1] One of its purposes is to extend the rich theory of monotone dynamical systems developed by Hirsch [8] see [11] for a review and [11, 1, 6, 10] for applications in biology. For biological applications of monotone I O systems see [5] and the use of small gain theorems in biology see [13]. 2 Preliminaries and proofs 2.1 Monotone I O systems and a small gain theorem The material in this section can be found in a far more general setting in [1, 2] We restrict to a framework that serves our purposes, namely I O systems described by di#erential equations. Consider the following ....
E.D. Sontag, Asymptotic amplitudes and Cauchy gains: A small-gain principle and an application to inhibitory biological feedback, Systems Control Lett. 47, 167-179 (2002).
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