Search results with tag "Lyapunov"
13 Lyapunov functions
www.ndsu.edumachinery of Lyapunov functions to establish that the origin is Lyapunov stable. As a candidate of Lyapunov function let me take V(x,y) = y2 2 +1−cosx. Note that in a small neighborhood of (0,0) my V is positive definite. Now V˙ (x,y) = ysinx+y(−sinx) = 0, and hence my V is an example of a Lyapunov function, but not strict Lyapunov ...
Lecture 13 Linear quadratic Lyapunov theory
web.stanford.edu• then solve a set of linear equations to find the (unique) quadratic form V(z) = zTPz • V will be positive definite, so it is a Lyapunov function that proves A is stable in particular: a linear system is stable if and only if there is a quadratic Lyapunov function that proves it Linear quadratic Lyapunov theory 13–11
Tools for Analysis of Dynamic Systems: Lyapunov s Methods
engineering.utsa.edu1 Tools for Analysis of Dynamic Systems: Lyapunov’s Methods Stanisław H. Żak School of Electrical and Computer Engineering ECE 680 Fall 2013
A Mathematical Introduction to Robotic Manipulation
www.cse.lehigh.edu4.1 Basic definitions . . . . . . . . . . . . . . . . . . . 179 4.2 The direct method of Lyapunov . . . . . . . . . . . 181 4.3 The indirect method of Lyapunov ...
OntheKroneckerProduct - Mathematics
www.math.uwaterloo.cations, such as the Sylvester equation: AX+XB = C, the Lyapunov equation: XA + A∗X = H, the commutativity equation: AX = XA, and others. In all cases, we want to know which matrices X satisfy these equations. This can easily be established using the theory of Kronecker products. A similar product, the symmetric Kronecker product, denoted by A ...
Chapter 8 An Introduction to Discrete Probability
www.cis.upenn.edusandr Lyapunov, Andrei Markov, Emile Borel, and Paul Levy should also be added´ ... is a finite set W of outcomes or elementary events w 2 W, together with a function Pr: W ! R, called probability measure (or probability distribution) satisfying the following properties: 0 Pr(w) 1 …
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math.unm.edu988 t,. E. KLOEDEN ANDJ. LORENZ forall ->0andall Xo A. Ifin additionthere exists a8o>0andforeach e>0atime T(e)>0 suchthat dist (x(t; Xo),A)<e forall >-T(e) wheneverdist(Xo,A)<o,wesaythat Ais uniformly asymptotically stable for (2.1). Lyapunov functions maybe used to characterize the stability of an arbitrarily shapedAforwhichthere is nosimple spectral theoryas whenAis asingletonset.