Estimation of the domain of attraction for saturated discrete-time systems

Álamo, T.; Cepeda, A.; Limón, Daniel; Camacho, Eduardo F.

doi:10.1080/00207720600784684

Cited by 33 publications

(13 citation statements)

References 17 publications

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“…Also shown in Fig. 2 is the smaller Lyapunov level curve which inscribes the forbidden point given before (x (1) ), as well as the desired limit cycle G = 0.…”

Section: Application 1: Oscillations In a Dc-dc Boost Convertermentioning

confidence: 79%

“…Notice that if the original Lyapunov theorem is used to prove global stability, the previous assumption is also fulfilled. Assumption 1 also guarantees local stability for system (1). The problem lies in the estimation of the domain of attraction.…”

Section: Assumptionmentioning

confidence: 99%

“…Furthermore, saturation‐like functions, which are one of the most common nonlinearities in practice, usually fall outside of the scope of these techniques. Saturations‐like functions are typically only considered in the case of linear systems , or in specific cases, such as in a port‐controlled Hamiltonian system .…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, saturation-like functions, which are one of the most common nonlinearities in practice, usually fall outside of the scope of these techniques. Saturations-like functions are typically only considered in the case of linear systems [1,4,17,19], or in specific cases, such as in a port-controlled Hamiltonian system [29]. This paper presents a simple idea that solves the problem of attraction domain estimation for polynomial nonlinear systems (among others) with saturation-like constraints and state constraints.…”

Section: Introductionmentioning

confidence: 99%

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Estimating the Attraction Domain for the Boost Inverter

Albea-Sánchez

Gordillo²

2012

Asian Journal of Control

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This work presents an approach for estimating the domain of attraction for polynomial systems with state and control‐signal constraints, including saturation. In many problems, it is possible to derive global stability properties for such systems, neglecting constraints. Consideration of the constraints usually makes the problem much more complicated. In this paper, the stability analysis performed for the unconstrained case is used for the problem as a whole. For application of the method, there are powerful computational tools that can be employed in cases of polynomial systems. The technique is not only valid for the analysis of equilibrium points, but also for other attractors, such as limit cycles. As examples, the domain of attraction for given control laws is estimated for both a nonlinear DC‐DC boost converter and for a boost inverter.

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“…Also shown in Fig. 2 is the smaller Lyapunov level curve which inscribes the forbidden point given before (x (1) ), as well as the desired limit cycle G = 0.…”

Section: Application 1: Oscillations In a Dc-dc Boost Convertermentioning

confidence: 79%

Section: Assumptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimating the Attraction Domain for the Boost Inverter

Albea-Sánchez

Gordillo²

2012

Asian Journal of Control

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“…The proof of the following lemma can be found in [16]. Lemma 1: Consider the ellipsoid E (P, 1) = {x : R n : x T Px ≤ 1}, with P = P T > 0.…”

Section: Capturing the Geometry Of The Local Invariant Setmentioning

confidence: 99%

On the computation of local invariant sets for nonlinear systems

Fiacchini

Álamo

Camacho

2007

2007 46th IEEE Conference on Decision and Control

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The importance of invariant sets in control is due to the fact that they define a region of the space where stability, and potentially asymptotic convergence, are assured. For this reason many control design strategies are related to the computation of an invariant set. This is particularly the case for receding horizon based strategies as model predictive control. This paper presents a method for computing a convex invariant set for nonlinear systems. Using properties of D.C. functions, which are functions that can be expressed as difference of two convex functions, and the fact that any continuous nonlinear function can be expressed as D.C. functions, or, at least, well approximated by them, we propose an algorithm for computing a polyhedral invariant set in which no global optimization problem has to be solved. The proposed strategy is guaranteed to provide a non-empty local invariant set provided the nonlinear system is locally stable.

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