Feedback Systems: Input-Output Properties

Desoer, C.; Vidyasagar, M.

doi:10.1115/1.3426967

Cited by 1,713 publications

(211 citation statements)

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“…Indeed, it is possible that, for fixed ξ , the right-hand side of (4.27) is converging to 1 as z → 0 or z → ∞. Therefore, rather than comparing Corollary 4.11 with classical small-gain theorems [11,13,14,23,45], it is more appropriate to view it in the context of "modern" nonlinear ISS small-gain results, see for example [10,21,36,43].…”

Section: Corollary 411 Let K ∈ S R (A B C) If F Satisfies (B ) Tmentioning

confidence: 99%

“…Note that (B ) is not a small-gain condition in the sense of classical input-output theory of feedback systems (as presented, for example, in [11,13,14,23,45]): whilst, for every fixed ξ ∈ im C, the right-hand side of (4.27) is smaller than 1 for all z = 0, it is in general not uniformly bounded away from 1. Indeed, it is possible that, for fixed ξ , the right-hand side of (4.27) is converging to 1 as z → 0 or z → ∞.…”

Section: Corollary 411 Let K ∈ S R (A B C) If F Satisfies (B ) Tmentioning

confidence: 99%

“…An absolute stability criterion for (1.1) is a sufficient condition for stability, usually formulated in terms of frequency-domain properties of the linear system given by (A, B, C) and sector or boundedness conditions for f , guaranteeing stability for all nonlinearities f satisfying these conditions. Traditionally, Lyapunov approaches to the stability theory of systems of the form (1.1) consider the uncontrolled (v = 0) case, whilst Lur'e systems with forcing (usually acting through B, that is, v is of the form v = Bw for some w) have been studied using the input-output framework initiated by Sandberg and Zames in the 1960s; see, for example, [11,45]. More recently, forced Lur'e systems have been analyzed in the context of input-to-state stability (ISS) theory, see [4,19,20,36].…”

Section: X(t) = Ax(t) + Bu(t) + V(t) Y(t) = C X(t) U(t) = F (Y(t))mentioning

confidence: 99%

See 2 more Smart Citations

The converging-input converging-state property for Lur’e systems

Bill¹,

Guiver²,

Logemann³

et al. 2017

Math. Control Signals Syst.

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Using methods from classical absolute stability theory, combined with recent results on input-to-state stability (ISS) of Lur'e systems, we derive necessary and sufficient conditions for a class of Lur'e systems to have the converging-input converging-state (CICS) property. In particular, we provide sufficient conditions for CICS which are reminiscent of the complex Aizerman conjecture and the circle criterion and connections are also made with small gain ISS theorems. The penultimate section of the paper is devoted to non-negative Lur'e systems which arise naturally in, for example, ecological and biochemical applications: the main result in this context is a sufficient criterion for a so-called "quasi CICS" property for Lur'e systems which, when uncontrolled, admit two equilibria. The theory is illustrated with numerous examples. Keywords Absolute stability · Circle criterion · Converging-input converging-state property · Input-to-state stability · Lur'e systems · Non-negative systems Mathematics Subject Classification

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Section: Corollary 411 Let K ∈ S R (A B C) If F Satisfies (B ) Tmentioning

confidence: 99%

Section: Corollary 411 Let K ∈ S R (A B C) If F Satisfies (B ) Tmentioning

confidence: 99%

Section: X(t) = Ax(t) + Bu(t) + V(t) Y(t) = C X(t) U(t) = F (Y(t))mentioning

confidence: 99%

See 1 more Smart Citation

The converging-input converging-state property for Lur’e systems

Bill¹,

Guiver²,

Logemann³

et al. 2017

Math. Control Signals Syst.

View full text Add to dashboard Cite

show abstract

“…[19]. Their extension to discrete-time is trivial, since they can be formulated in abstract Hilbert spaces for inputs and outputs, similarly as the passivity theorem is given in [15].…”

Section: Full Resetmentioning

confidence: 99%

Towards -stability of discrete-time reset control systems via dissipativity theory

Carrasco

Navarro-López

2013

Systems & Control Letters

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This paper proposes conditions on input-output stability of discrete-time reset systems by using some key dissipativity properties. In the continuoustime setting, dissipativity of the base linear system is preserved under reset actions if the storage function is decreasing at reset times. Indeed, when the reset system is full reset, the dissipativity of the base linear system ensures the dissipativity of the reset system. However, in the discrete-time setting, this condition on the storage function is not enough to ensure the dissipativity of the base linear system. We define some dissipativity properties of discretetime reset systems and give an appropriate definition of the reset system in order to preserve the (Q, S, R)−dissipativity of the base linear system under reset actions. As a result, ℓ 2 -stability of feedback interconnected dissipative control reset systems is obtained.

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“…Another approach to stabilize non-linear systems is based on the Gronwall-Bellman lemma (see Pachpatte, 1973;Desoer and Vidyasagar, 1975). For example, this lemma has been applied to the exponential stability of non-linear affine systems by Zevin and Pinsky (2003), non-linear observer synthesis by Shimizu (2000), robust stabilization and observation of non-linear uncertain systems byŻak (1990), and robust stability of linear systems by Chen and Wong (1987) and Jetto and Orsini (2007).…”

Section: Introductionmentioning

confidence: 99%

On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

Ndoye

Darouach

Voos

et al. 2015

IMA J Math Control Info

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This paper presents the robust stabilization problem of linear and non-linear fractional-order systems with non-linear uncertain parameters. The uncertainty in the model appears in the form of the combination of 'additive perturbation' and 'multiplicative perturbation'. Sufficient conditions for the robust asymptotical stabilization of linear fractional-order systems are presented in terms of linear matrix inequalities (LMIs) with the fractional-order 0 < α < 1. Sufficient conditions for the robust asymptotical stabilization of non-linear fractional-order systems are then derived using a generalization of the Gronwall-Bellman approach. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.

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Feedback Systems: Input-Output Properties

Cited by 1,713 publications

References 0 publications

The converging-input converging-state property for Lur’e systems

The converging-input converging-state property for Lur’e systems

Towards -stability of discrete-time reset control systems via dissipativity theory

On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

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