Application To Stability
In the following theorems, and and are symmetric. The notation means that the matrix is positive definite
Theorem (continuous time version). If there exist and satisfying then the linear system is globally asymptotically stable. The quadratic function is a Lyapunov function that can be used to verify stability.
Theorem (discrete time version). If there exist and satisfying then the linear system is globally asymptotically stable. As before, is a Lyapunov function.
Read more about this topic: Lyapunov Equation
Famous quotes containing the words application to, application and/or stability:
“Preaching is the expression of the moral sentiment in application to the duties of life.”
—Ralph Waldo Emerson (1803–1882)
“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Every nation ... whose affairs betray a want of wisdom and stability may calculate on every loss which can be sustained from the more systematic policy of its wiser neighbors.”
—James Madison (1751–1836)