Lyapunov
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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 ...
Tools for Analysis of Dynamic Systems: Lyapunov s Methods
engineering.utsa.eduLyapunov Stability Game The adversary picks a region in the state space of radius ε You are challenged to find a region of radius δ such that if the initial state starts out inside your region, it remains in his region---if you can do this, your system is stable, in the sense of Lyapunov
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 ...
Ordinary Differential Equations: Graduate Level Problems ...
www.math.ucla.eduOrdinary Differential Equations Igor Yanovsky, 2005 2 Disclaimer: This handbook is intended to assist graduate students with qualifying examination preparation.