Analysis of hybrid systems’ dynamics using the common Lyapunov functions and multiple homomorphisms

Vassilyev, S. N.; Kosov, A. A.

doi:10.1134/s000511791106004x

Cited by 35 publications

(9 citation statements)

References 10 publications

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“…9,[39][40][41][42] In order to compute inner estimates of domains of attraction of switched systems, researchers have proposed two classical methodologies. One is common Lyapunov functions based technique 39,43,44 and the other is multiple Lyapunov functions based technique. 24,45 Computing suitable (common and multiple) Lyapunov functions is difficult due to the nonlinearity of systems.…”

Section: Introductionmentioning

confidence: 99%

Computing multiple Lyapunov‐like functions for inner estimates of domains of attraction of switched hybrid systems

Zheng

She

et al. 2018

Intl J Robust & Nonlinear

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Summary Domain of attraction plays an important role in stability analysis and safety verification of nonlinear control systems. In this paper, based on the concept of multiple Lyapunov‐like functions, we propose iteration algorithms for computing inner estimates of domains of attraction for a class of switched hybrid systems, where the state space is composed of several regions and each region is described by polyhedral sets. Starting with an initial inner estimate of domain of attraction, we firstly present a theoretical framework for obtaining a larger inner estimate by iteratively computing multiple Lyapunov‐like functions. Successively, the theoretical framework is underapproximatively realized by using S‐procedure and sums of squares programming, associated with the coordinatewise iteration method. Afterwards, for obtaining a required initial inner estimate of domain of attraction, we propose an alternative higher‐order truncation and linear semidefinite programming based method for computing a common Lyapunov function. Especially, a bisection method based improvement is proposed for obtaining better estimates in each iteration step. Finally, we implement proposed algorithms and test them on numerical examples with comparisons. These computation and comparison results show that the advantages of our multiple Lyapunov‐like functions based algorithm. Especially, we provide alternative underapproximations for avoiding the possible numerical problem.

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Section: Introductionmentioning

confidence: 99%

Computing multiple Lyapunov‐like functions for inner estimates of domains of attraction of switched hybrid systems

Zheng

She

et al. 2018

Intl J Robust & Nonlinear

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“…Further studies of this problem have led to the development of systems with variable structure [5]. Presently, this trend developed into the theory of hybrid (switched) control systems combining the properties of continuous and discrete systems [6][7][8]. There are the potentialities of the formation of complex nonlinear control rules in the switched systems, which change depending on the changing external factors of the environment.…”

Section: Actuality Of Multi-alternative Controlmentioning

confidence: 99%

Multi-alternative control of large systems

Podvalny

Vasiljev

2018

MATEC Web Conf.

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Abstract. The article deals with analysis of evolutionary concept of control of large systems -multialternativeness. Based on the biocybernetical approach to the task we are revealing information components of this concept, which is formulated in the following 3-M principles: multilevel structure is implementing in complex systems as the property of homeostasis; multi-version of algorithms and separation of control functions for the adaptive systems control; modularity as guarantee for this diversity.

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“…For any values of c > a, we have pairs of ovals situated symmetrically on both sides of the real axis, the maximal width of the ovals being (a/ √ c), the height of ovals being ( √ c + a − √ c − a). We consider now on the complex plane a closed region bounded by curve (13). It is given bȳ…”

Section: Modified Cassini Oval Regionsmentioning

confidence: 99%

“…The Lyapunov matrix equation of matrix root-clustering was generalized in [1,5]. The problem of root clustering is topical for the robust control systems [10][11][12][13][14][15] and control of the multiagent systems [16].…”

Section: Introductionmentioning

confidence: 99%

Method of forbidden regions in the dynamic system matrices root clustering problem

Melnikov

Dudarenko

2014

Autom Remote Control

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New criteria for root-clustering of the dynamic system matrices in multiply connected regions were presented. A concept of the forbidden region was introduced, and a generalization of the Lyapunov-Jury theorem onto the multiply connected regions was proposed. The necessary and sufficient conditions for root-clustering outside the forbidden region were established as a sequence of matrix inequalities. Construction of the conditions for root-clustering outside the frequency bands and robust root-clustering in multiply connected region was illustrated by way of examples.

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Analysis of hybrid systems’ dynamics using the common Lyapunov functions and multiple homomorphisms

Cited by 35 publications

References 10 publications

Computing multiple Lyapunov‐like functions for inner estimates of domains of attraction of switched hybrid systems

Computing multiple Lyapunov‐like functions for inner estimates of domains of attraction of switched hybrid systems

Multi-alternative control of large systems

Method of forbidden regions in the dynamic system matrices root clustering problem

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