2012
DOI: 10.1109/tac.2011.2179869
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Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems

Abstract: Nonlinear control algorithms of two types are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into selected neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode contr… Show more

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Cited by 3,450 publications
(1,642 citation statements)
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References 23 publications
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“…Some results in this context can be discovered in the literature. In particular, fast stability of ODEs is represented by the notions of finite-time and fixed-time stabilities [50], [43], [20], [11], [6], [29], [26], [2], [14], [33], [39], but hyper exponential transitions are studied in [38] as fast behavior of time delay systems. Fast models described by partial differential equations may demonstrate the so-called finite-time extinction property [46], [19], [31], [10] also known as super stability [5], [13].…”
Section: State Of the Artmentioning
confidence: 99%
See 2 more Smart Citations
“…Some results in this context can be discovered in the literature. In particular, fast stability of ODEs is represented by the notions of finite-time and fixed-time stabilities [50], [43], [20], [11], [6], [29], [26], [2], [14], [33], [39], but hyper exponential transitions are studied in [38] as fast behavior of time delay systems. Fast models described by partial differential equations may demonstrate the so-called finite-time extinction property [46], [19], [31], [10] also known as super stability [5], [13].…”
Section: State Of the Artmentioning
confidence: 99%
“…Definition 9 (Fixed-time stability, [33]). The origin of the system (1) is said to be fixed-time stable if it is uniformly finite-time stable in U ⊂ R n and the settling time function T (t 0 , x 0 ) is bounded on R ×U, i.e.…”
Section: Non-asymptotic Convergencementioning
confidence: 99%
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“…For an initial condition x 0 ∈ R n , denote the corresponding solution by X(t, x 0 ) for any t ≥ 0 for which the solution exists. Following [3], [19], [20], let Ω be an open neighborhood of the origin in R n .…”
Section: Preliminariesmentioning
confidence: 99%
“…The initial conditions of this system are x(0) = x 0 . Definition 2.1 (Global finite-time stability [9]): The origin of (1) is globally finite-time stable if it is globally asymptotically stable and any solution x(t, x 0 ) of (1) reaches the equilibrium point at some finite time moment, i.e., ∀t…”
Section: Mathematical Preliminaries Consider the Systemẋmentioning
confidence: 99%