2.4. Relevant theorems and lemmas on finite-time stability for autonomous systems. The following theorem gives necessary and sufficient conditions for finite-time stability of autonomous systems. Theorem 2. Let us consider system with uniqueness of solutions in forward time outside the origin. The following properties are equivalent: (1)
FINITE-TIME STABILITY OF CONTINUOUS AUTONOMOUS SYSTEMS SANJAY P. BHATyAND DENNIS S. BERNSTEINz SIAM J. CONTROL OPTIM. °c 2000 Society for Industrial and Applied Mathematics Vol. 38, No. 3, pp. 751-766 Abstract. Finite-time stability is de ned for equilibria of continuous but non-Lipschitzian
ﬁnite-time stability, which gives a necessary and sufﬁcient condition for non-Lipschitz continuous autonomous systems to be ﬁnite-time stable [15,18,19,26,27]. Deﬁnition 1. (Bhat and Bernstein 2000 ) Consider the non-Lipschitz continuous autonomous system on the open neighborhood D of the origin x = 0 , f : D !Rn, such that
The objective of this book is to present systematic methods for achieving stable, agile and efficient locomotion in bipedal robots. The fundamental principles presented here can be used to improve the control of existing robots and provide guidelines for improving the mechanical design of future robots.
Finite time stability is investigated for continuous system x ˙ = f (x) which satisfies uniqueness of solutions in forward time. A necessary and sufficient condition for finite time stability is given for this class of systems using Lyapunov functions.
CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. Finite-time stability is dened for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Hölder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov re-sults involving scalar dierential ...
Conditions for Fixed-Time Stability and Stabilization of Continuous Autonomous Systems Francisco Lopez-Ramirez 1, Denis E mov;2, Andrey Polyakov and Wilfrid Perruquetti3 1Inria, Univ. Lille, CNRS, UMR 9189 - CRIStAL, F-59000 Lille, France. 2ITMO University, 49 Kronverkskiy av., 197101 Saint Petersburg, Russia. 3Ecole Centrale de Lille, Cit e Scienti que, 59651 Villeneuve d’Ascq Cedex, France.
The main result that links homogeneity and finite-time stability is that a homogeneous system is finite-time stable if and only if it is asymptotically stable and has a negative degree of homogeneity. We also show that the assumption of homogeneity leads to stronger properties for finite-time stable systems.
In this paper, we investigate the problem of finite-time stability (FTS) of linear non-autonomous systems with time-varying delays. By constructing an appropriated function, we derive some explicit conditions in terms of matrix inequalities ensuring that the state trajectories of the system do not exceed a certain threshold over a pre-specified finite time interval.
Abstract. This paper investigates the finite-time stability problem for a class of discrete-time switched linear systems with impulse effects. Based on the average dwell time approach, a sufficient condition is established which ensures that the state trajectory of the system remains in a bounded region of the state space over a pre-specified finite time interval.
Citation: Bhat, Sanjay P.; Bernstein, Dennis S. (2000). "FINITE-TIME STABILITY OF CONTINUOUS AUTONOMOUS SYSTEMS." SIAM Journal of Control and Optimization, Vol. 38 ...
This paper studies the finite-time stability problem of a class of switched nonlinear systems with state constraints and control constrains. For each subsystem, optimization controller is designed by choosing the appropriate Lyapunov function to stabilize the subsystem in finite time and the estimation of the region of attraction can be prescribed.
Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are ...
Abstract. Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are studied and illustrated with several examples.
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This paper deals with finite time inverse optimal stabilization for stochastic nonlinear systems. A concept of the stochastic finite time control Lyapunov function (SFT-CLF) is presented, and a control law for finite time stabilization for the closed-loop system is obtained. ... “Finite-time stability of continuous autonomous systems,” SIAM ...
Abstract. Finite time stability is defined for continuous non autonomous systems. Starting with a result from Haimo Haimo (1986) we then extend this result to n¡dimensional non autonomous systems through the use of smooth and nonsmooth Lyapunov functions as in Perruquetti and Drakunov (2000).
Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Hölder continuity of the settling-time function are studied and illustrated with several examples.
In this paper, we study finite-time stability of continuous non-autonomous sys-tems. Through the finite-time stability analysis of continuous time-varying scalar systems ...
March 22, 2007 9:45 International Journal of Control IJCFiniteTime Finite time stability conditions for non autonomous continuous systems 3 A1) the origin is Lyapunov stable for the system (3),