Vector norms as Lyapunov functions for linear systems

A unified theory of quadratic and piecewise-linear Lyapunov functions for continuous and discrete-time linear systems is presented. The key to this work is the description of these Lyapunov functions by vector norms. The main results are sufficient and necessary conditions for a vector norm to be a Lyapunov function as well as a method (based on these conditions) of constructing such Lyapunov functions.<
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