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
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