Finite-Time Stability of Continuous Autonomous Systems

By Sanjay P. Bhat, Dennis S. Bernstein. SIAM Journal of Control and Optimization, 2000

5,062 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/2928d412fc4736a29194e5432f59744dced7a469

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Shaocheng Tong
2. Andrey E. Polyakov
3. Xinghuo Yu
4. Zongyu Zuo
5. Yong-ming Li
6. Qing-Long Han
7. Peng Shi
8. Xu Jin

Citations in the corpus

• Sliding Mode Direct Yaw-Moment Control Design for In-Wheel Electric Vehicles (2017, methodology): “According to the finite-time Lyapunov stability theory proposed in [32], the sliding variable s will converge to the origin in a finite time.”
• Fixed/Preassigned-Time Synchronization of Complex Networks via Improving Fixed-Time Stability (2020, background): “INTRODUCTION F IXED-TIME (FXT) stability was initially proposed by Polyakov in 2012 [1] to eliminate the dependence of the settling time (ST) on initial values in finite-time (FNT) stability [2].”
• On an output feedback finite-time stabilization problem (2001, background): “The authors also wish to thank S. Bhat and D. Bernstein for providing a preprint of [ 5 ].”
• Nonsingular fixed-time consensus tracking for second-order multi-agent networks (2015, background): “The benchmark work due to Bhat and Bernstein (2000) related the regularity properties of the Lyapunov functions to the settling time function in finite-time stability analysis for autonomous systems.”
• Technical Notes and Correspondence Uniformly Observable and Globally Lipschitzian Nonlinear Systems Admit Global Finite-Time Observers (2009, methodology): “Lemma 1: [ 2 ]: Suppose there exist a positive definite continuous function , real numbers , and an open neighborhood of the origin such that”
• Finite time stability and stabilization of a class of continuous systems (2006, methodology): “We could refer to a result given in [5] in order to use a necessary and sufficient condition involving a Lyapunov function only.”
• Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems (2012, background): “The finite-time stability property may demonstrate homogeneous systems with negative degree [4], [20] or the so-called sliding homogeneous systems [16].”
• Monotone Approximations of Minimum and Maximum Functions and Multi-objective Problems (2012, background): “As a consequence the pursuers’ goal function is first increasing with time (unlike in the standard Liapunov functions analysis) and then decreases in a way similar to finite-time stability convergence [4], which is not surprising given that the players’ control strategies are computed using expressi”
• Distributed Control Strategies for Microgrids: An Overview (2020, background): “Regarding finite-time consensus, this technique allows achieving convergence in a finite number of steps [99], [100], while rejecting disturbances and dealing with uncertainties [161].”
• Almost global finite‐time stabilization of rigid body attitude dynamics using rotation matrices (2016, background): “While the work in [16] dealt with continuous finite-time control schemes and the work in [15] dealt with double integrator dynamics, a constructive way to obtain continuous finite-time stabilizing control for mechanical systems with multiple degrees of freedom appeared recently in [29].”
• Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics (2018, background): “In practice, finite-time convergence is more preferable due to its tracking accuracy and better disturbance rejection [10], which therefore triggers an intensive research on finite-time cooperation control.”
• Neural Networks-Based Adaptive Finite-Time Fault-Tolerant Control for a Class of Strict-Feedback Switched Nonlinear Systems (2019, background): “Lemma 1 [63], [64]: Suppose V(x) is a C1 smooth positivedefinite function (defined on U ⊂ Rn) and V̇(x) + λV(x) is a negative semi-definite function on U ⊂ Rn for α ∈ (0, 1) and λ ∈ R+, then there exists an area U0 ⊂ Rn such that any V(x) which starts from U0 ⊂ Rn can reach V(x) ≡ 0 in finite time.”
• Distributed Finite-Time Average Consensus in Digraphs in the Presence of Time Delays (2015, background): “Finite-time consensus algorithms are, in general, more desirable; besides the fact that they converge in finite time, it is reported that closed-loop systems under finite-time control usually demonstrate better disturbance rejection properties [22]; this can be important in applications where the…”
• Adaptive Fixed-Time Control for MIMO Nonlinear Systems With Asymmetric Output Constraints Using Universal Barrier Functions (2019, background): “Compared with conventional finite-time control methods, for example, [10] and [11], the convergence time estimation of fixed-time or prescribed finite-time control algorithms does not depend on the initial conditions [1], [6]–[9], and can be predefined according to the user specifications.”