Classification of stability-like concepts and their study using vector Lyapunov functions

Habets, Patrick; Peiffer, Karl

doi:10.1016/0022-247x(73)90090-5

Cited by 17 publications

(4 citation statements)

References 13 publications

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“…Thus the work is of a very general nature. (For unification in a different direction see (19) It is shown that our results on the stability properties can be extended to cover control systems with the set of controls compact in R m .…”

Section: Introductionmentioning

confidence: 99%

The General Stability – Like Concepts for Differential and Control System

B.S.¹

2022

ijmcr

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Theorems corresponding to the concepts of stability discussed in the works under reference should follow the general pattern of the direct method of Lyapunov. Theorems proved for such stability contain, as special cases results on - (i) stability for the origin, (ii) stability with respect to some components, (iii) stability of a set A, (iv) stability of a set A (t), (v) stability of conditional invariant set B relative to A, (vi) Stability of asymptotic invariant set A and (vii) stability of conditional asymptotic invariant set B relative to A. It is shown that our results on the stability properties can be extended to cover control systems with the set of controls compact in Rm.

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Section: Introductionmentioning

confidence: 99%

The General Stability – Like Concepts for Differential and Control System

B.S.¹

2022

ijmcr

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“…There are many approaches for the decomposition and aggregation of large-scale systems [1,4,5,7,8,13,14,16,18,22]. These approaches are especially well developed for the construction of linear comparison systems [1,4,5,16].…”

Section: Introductionmentioning

confidence: 99%

Aggregation and stability analysis of nonlinear complex systems

Aleksandrov

Платонов

2008

Journal of Mathematical Analysis and Applications

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The problem of stability of large-scale systems in critical cases is investigated. New form of aggregation for essentially nonlinear complex systems is suggested. With the help of this form the sufficient conditions of asymptotic stability are determined. The results obtained are used for the stability analysis of complex systems by the nonlinear approximation and for the investigation of absolute stability conditions for a certain class of nonlinear systems.

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“…Similar types of generalized dynamical systems were considered in a few works in the literature. One of the initial treatments of such systems appeared in [7] where dynamical systems in general spaces were introduced as generalized pseudo-dynamical systems and stability results were presented (inspiration for the work in [7] was drawn from the observations in [5]). In a series of subsequent articles, a type of limit sets pertaining to the reachable set and the prolongational limit of solutions to such systems were studied in [8] and [9]; see also [12].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic properties of solutions to set dynamical systems

Sanfelice

2014

53rd IEEE Conference on Decision and Control

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Dynamical systems with trajectories given by sequences of sets are studied. For this class of generalized systems, notions of solution, invariance, and omega limit sets are defined. The structural properties of omega limit sets are revealed. In particular, it is shown that for complete and bounded solutions, the omega limit set of a bounded and complete solution is nonempty, compact, and forward invariant. Lyapunov-like conditions to locate omega limit sets are also derived. Tools from the theory of set convergence are conveniently used to prove the results. The findings are illustrated in several examples and applications, including the computation of reachable sets and forward invariant sets, and propagation of uncertainty.

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Classification of stability-like concepts and their study using vector Lyapunov functions

Cited by 17 publications

References 13 publications

The General Stability – Like Concepts for Differential and Control System

The General Stability – Like Concepts for Differential and Control System

Aggregation and stability analysis of nonlinear complex systems

Asymptotic properties of solutions to set dynamical systems

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