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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 ...
Lecture 13 Linear quadratic Lyapunov theory
web.stanford.edu• evaluating quadratic integrals • analysis of ARE • discrete-time results • linearization theorem 13–1. The Lyapunov equation the Lyapunov equation is ... 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