Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems

By Andrey E. Polyakov. IEEE Transactions on Automatic Control, 2012

4,366 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/6ba46ff4b16f7e9831d035871053fed9fcf201ed

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In Control and Systems Engineering

Citations in the corpus

Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time (2017, background): “Polyakov (2012) developed fixed-time designs for linear controllable systems.”
Adaptive Fuzzy Practical Fixed-Time Tracking Control of Nonlinear Systems (2021, background): “…for the ﬁxed-time control, one of the most notable achievements is that the practical ﬁxed-time stability was concluded from the inequalities in the form of ˙ V ( x ) ≤ − ( μ 1 V ( x ) α + μ 2 V ( x ) β ) γ + (cid:2) with μ 1 , μ 2 , α, β, γ ∈ R, αγ < 1 and βγ > 1 (see [10], [14], and [15]).”
Fixed-time stabilization and consensus of nonholonomic systems (2016, neutral): “The fixed-time control algorithm [35] has the form u = −(|x|2 + 1)sign(x).”
Fixed-Time Attitude Control for Rigid Spacecraft With Actuator Saturation and Faults (2016, background): “Thus, in contrast to existing finite-time controllers, the upper bound of the settling time could be estimated independent of initial conditions, in the sense of the fixed-time stability concept [15].”
Finite-time and fixed-time stabilization: Implicit Lyapunov function approach (2015, background): “See Polyakov (2012) or Polyakov and Fridman (2014) for more details.”
Adaptive Fixed-Time Control for MIMO Nonlinear Systems With Asymmetric Output Constraints Using Universal Barrier Functions (2019, background): “However, among the limited amount of works available in the literature on the fixed-time control techniques, most of them address only linear systems [2], or systems in the form of pure-integrators with limited discussions on the system uncertainties and disturbances [3], [4].”
Terminal Sliding Mode Control – An Overview (2021, background): “ous mathematical proof of the fixed-time convergence is found in [22].”
Prescribed-Time Control and Its Latest Developments (2022, background): “Later on, a notion termed fixed-time (FxT) control [83], [84], [85], [86], [87], [88], [89], [90], [91], [92] has emerged, which employs odd-order plus fractional-order feedback to provide various”
Fixed/Preassigned-Time Synchronization of Complex Networks via Improving Fixed-Time Stability (2020, methodology): “It is shown that the established conditions in this article are more relaxed and the estimates for ST are more accurate in comparison with the existing results [1], [9].”
A fixed-time output feedback control scheme for double integrator systems (2017, methodology): “Definition 7 [13] The origin of system (1) is said to be fixed-time stable if it is globally finite-time stable and there exists a fixed positive constant Tmax such that T ≤ Tmax for any x0 ∈ R.”
Robust stabilization of MIMO systems in finite/fixed time (2016, methodology): “In the paper [6] it was proven that the orthogonal matrix”
Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics (2018, background): “Lemma 1: [18], [19] If there exists a continuous radially unbounded and positive definite function V (x) such that V̇ (x) ≤ −αV p (x) − βV q (x) (2) for some α, β > 0, p > 1, 0 < q < 1, then the origin of this system (1) is globally fixed-time stable and the settling time function T can be estimated”