Practical Stability of a Moving Robot with Respect to Given Domains

Martynyuk, À. À.; Khoroshun, À. S.; Chernienko, A. N.

doi:10.1007/s10778-014-0613-2

Cited by 7 publications

(2 citation statements)

References 9 publications

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“…After Kamenkov's introduction, the concept of FTS was developed in the sixties in [6][7][8][9][10][11]. In the following years, several other results were proposed on this topic using the alternative terms of stability over finite interval or practical stability [12][13][14][15]. However, most of the techniques presented in that period both for the analysis [16][17][18] and for the design of finite-time stable control systems [19,20] were computationally cumbersome.…”

Section: Introductionmentioning

confidence: 99%

New conditions for finite‐time stability of impulsive dynamical systems via piecewise quadratic functions

Ambrosino

Ariola

Garone

et al. 2022

IET Control Theory & Appl

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In this paper, the use of time‐varying piecewise quadratic functions is investigated to characterize the finite‐time stability of state‐dependent impulsive dynamical linear systems. Finite‐time stability defines the behavior of a dynamic system over a bounded time interval. More precisely, a system is said to be finite‐time stable if, given a set of initial conditions, its state vector does not exit a predefined domain for a certain finite interval of time. This paper presents new sufficient conditions for finite‐time stability based on time‐varying piecewise quadratic functions. These conditions can be reformulated as a set of Linear Matrix Inequalities that can be efficiently solved through convex optimization solvers. Different numerical analysis are included in order to prove that the presented conditions are able to improve the results presented so far in the literature.

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Section: Introductionmentioning

confidence: 99%

New conditions for finite‐time stability of impulsive dynamical systems via piecewise quadratic functions

Ambrosino

Ariola

Garone

et al. 2022

IET Control Theory & Appl

View full text Add to dashboard Cite

show abstract

“…These types of stability are addressed in [2,3,10]. These types of stability were also used in [13] to solve specific problems of robotics. Grujic [7,8] proposed the concept of finite-time stability with fixed settling time, which is important for many problems of automatic control.…”

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confidence: 99%

Revisiting the Theory of Stability over a Finite Interval

Martynyuk

Khoroshun

2014

Int Appl Mech

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A method for analyzing contractive stability over a finite interval with fixed settling time is proposed. The method employs a Lyapunov-type function and analyzes its behavior along the trajectories of the system.Keywords: contractive stability, settling time, stability over finite interval, Lyapunov-type function Introduction. The theory of stability of motion proposed and developed by Lyapunov [1] and many other scientists deals with systems operating over an infinite time interval and assumes that that the initial and, hence, subsequent perturbations are rather small. However, dynamic problems for machines and many applied problems are solved considering that the corresponding mechanical systems operate over finite time intervals. Moreover, in analyzing finite-time stability, it is important not only to take into account the fact that there exists d for a given e, but also to estimate the initial and subsequent deviations because, by the theorem on continuous dependence of solutions on initial conditions, it is always possible to find a small perturbation to the initial conditions to satisfy the stability conditions on a prescribed time interval over which the system operates. It is also important whether the initial and subsequent deviations are suitable for the problem under consideration. Taking these issues into account leads to some new types of stability such as technical stability, finite-time stability, etc. [4][5][6]14]. These types of stability are addressed in [2,3,10]. These types of stability were also used in [13] to solve specific problems of robotics. Grujic [7,8] proposed the concept of finite-time stability with fixed settling time, which is important for many problems of automatic control.Contractive finite-time stability [3] with certain settling time is addressed below. 1. Problem Formulation. Consider a system of differential equations of perturbed motion:

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On Navigation Sensor Error Correction

Larin

2016

Int Appl Mech

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Practical Stability of a Moving Robot with Respect to Given Domains

Cited by 7 publications

References 9 publications

New conditions for finite‐time stability of impulsive dynamical systems via piecewise quadratic functions

New conditions for finite‐time stability of impulsive dynamical systems via piecewise quadratic functions

Revisiting the Theory of Stability over a Finite Interval

On Navigation Sensor Error Correction

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