Asymptotic stabilization of nonlinear systems using passivity indices

Madeira, Diego de S.; Adamy, Jürgen

doi:10.1109/acc.2016.7525073

Cited by 9 publications

(3 citation statements)

References 16 publications

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“…In [16], the authors addressed local passivity analysis. Furthermore, a dissipativity-based stabilisable output feedback synthesis is proposed in [17]- [19] based on the analysis of the passivity indices using the standard dissipativity relation. In [16]- [18], a sum-of-square (SOS) relaxation technique is adopted to solve the nonlinear dissipativity relation for polynomial nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike in [17]- [19] where dissipativity-based output feedback synthesis is considered for a class of nonlinear (timeinvariant) systems, we cope with computational output projection synthesis to ensure strict passivity and hence stable dynamic invertibility of rational strictly proper (D = 0) LPV models. Strict passivity of a dynamical system is a stronger property than the passivity indices-based dissipativity condition considered in [17]- [19]. In other words, strict passivity ensures the existence of a positive output feedback passivity index and a non-positive input feed-forward passivity index.…”

Section: Introductionmentioning

confidence: 99%

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Passivity analysis of rational LPV systems using Finsler’s lemma

Polcz

Kulcsár

Péni

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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In this paper, we show and utilize new results on the relationship between passivity, zero dynamics and stable dynamic invertibility of linear parameter-varying (LPV) systems. Furthermore, an optimization-based systematic passivity analysis procedure and a passivating output projection are proposed for asymptotically stable rational LPV systems in the linear fractional representation (LFR) form having at least as many independent output signals as input signals. The storage function is searched in a quadratic form with a symmetric rational parameter-dependent matrix. In order to form a square system and then to satisfy the Kalman-Yakubovich-Popov (KYP) properties, a parameter-dependent output projection matrix is searched in the LFR form. The nonlinear parameter dependence from the linear matrix inequality (LMI) and equality (LME) conditions provided by the KYP lemma is factorized out using the linear fractional transformation (LFT). Then, Finsler's lemma and affine annihilators are used to relax the sufficient affine parameter-dependent LMI and LME conditions. As an application example, a stable system inversion is addressed and demonstrated on a benchmark rational LPV model.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Passivity analysis of rational LPV systems using Finsler’s lemma

Polcz

Kulcsár

Péni

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

show abstract

“…These two numbers can be either positive or negative, where a negative value implies a shortage of passivity while a positive value implies an excess. Passivity indices are rather useful in the analysis of nonlinear and interconnected systems; for instance, [14,15] showed that the feedback interconnection of two non-passive systems is finite gain L 2 stable provided that the shortage of passivity of one component can be compensated for by the excess of passivity of another component, [27] provided a controller design method for asymptotic stabilization of a class of nonlinear systems using passivity indices, and [48] and [49] presented conditions on passivity indices of a closed-loop system in the continuous-time setting and with the event-triggered mechanism, respectively.…”

Section: Introductionmentioning

confidence: 99%

Passivity-Based Analysis of Sampled and Quantized Control Implementations

Xu,

Ozay,

Gupta

2018

Preprint

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This paper studies the performance of a continuous controller when implemented on digital devices via sampling and quantization, by leveraging passivity analysis. Degradation of passivity indices from a continuous-time control system to its sampled, input and output quantized model is studied using a notion of quasi-passivity. Based on that, the passivity property of a feedback-connected system where the continuous controller is replaced by its sampled and quantized model is studied, and conditions that ensure the state boundedness of the interconnected system are provided. Additionally, the approximate bisimulation-based control implementation where the controller is replaced by its approximate bisimilar symbolic model whose states are also quantized is analyzed. Several examples are provided to illustrate the theoretical results.

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Passivity-based analysis of sampled and quantized control implementations

Özay

Gupta

2020

Automatica

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Asymptotic stabilization of nonlinear systems using passivity indices

Cited by 9 publications

References 16 publications

Passivity analysis of rational LPV systems using Finsler’s lemma

Passivity analysis of rational LPV systems using Finsler’s lemma

Passivity-Based Analysis of Sampled and Quantized Control Implementations

Passivity-based analysis of sampled and quantized control implementations

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