A contraction approach to input tracking via high gain feedback

Hamadeh, Abdullah; Sontag, Eduardo D.; Vecchio, Domitilla Del

doi:10.1109/cdc.2015.7403435

Cited by 5 publications

(4 citation statements)

References 33 publications

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“…The reduced system (25) is a high-gain negative feedback interconnection of two SPR systems. Such systems have been studied in [15], where it has been shown that x 1 − ũ(t)/α a = O( √ ). Therefore, by triangle inequality, z 1 − ũ(t)/α a = O( √ ).…”

Section: Discussionmentioning

confidence: 99%

“…Lemma 2: (Theorem 1 in [15].) Consider an LTI system ẋ = Ax + Bu(t) with input u(t), and suppose that for a real matrix Q > 0, there exists c > 0 such that µ Q (A) ≤ −c.…”

Section: B Iss Property Of the Slow Error Systemmentioning

confidence: 99%

“…Proof: (Sketch.) Theorem 2 in [15] establishes that tracking error of a high-gain (1/ ) negative feedback interconnection of two SPR systems is O( √ ). With reference to Fig.…”

Section: Error Between the Full And The Reduced Systemsmentioning

confidence: 99%

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A Singular Singular Perturbation Problem Arising From a Class of Biomolecular Feedback Controllers

Qian

Vecchio

2019

IEEE Control Syst. Lett.

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A long-standing challenge in synthetic biology is to engineer biomolecular systems that can perform robustly in highly uncertain cellular environments. Recently, there has been increasing interest to design biomolecular feedback controllers to address this challenge. Molecular sequestration is one of the proposed feedback mechanisms. For this type of design, when all reactions within the controller are sufficiently fast, the process output can reach a set-point regardless of parametric uncertainties and constant disturbances. However, as we demonstrate in this paper, the way in which molecular sequestration affects the fast controller dynamics leads to a singular singularly perturbed (SSP) system. In an SSP system, the boundary layer Jacobian is singular and thus standard singular perturbation approaches cannot be applied, posing difficulties to analytically determine the performance of sequestrationbased controllers. In this paper, we consider a class of linear systems that capture the key structure of sequestration-based controllers. We show that, under certain technical conditions, these SSP systems can still be approximated by reduced-order systems that are dependent on the small parameter. This result allows us to analytically evaluate the tracking performance of the linearized model of a sequestration-based controller.

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Section: Discussionmentioning

confidence: 99%

“…Lemma 2: (Theorem 1 in [15].) Consider an LTI system ẋ = Ax + Bu(t) with input u(t), and suppose that for a real matrix Q > 0, there exists c > 0 such that µ Q (A) ≤ −c.…”

Section: B Iss Property Of the Slow Error Systemmentioning

confidence: 99%

See 1 more Smart Citation

A Singular Singular Perturbation Problem Arising From a Class of Biomolecular Feedback Controllers

Qian

Vecchio

2019

IEEE Control Syst. Lett.

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“…, z N (t) T ] T and d(t) being the stack of all d i 's (if the disturbance does not affect the i-th vehicle, then d i (t) = 0). Now, following Theorem A in (Desoer and Haneda, 1972) (see also Theorem 3 in (Hamadeh et al, 2015) for a self-contained proof), the dynamics of Z(t) can be expressed aṡ X), . .…”

Section: Proof Of Theoremmentioning

confidence: 99%