The recently developed technique for computation of piecewise quadratic Lyapunov functions is specialized to Lyapunov functions that are piecewise linear. This establishes a unified framework for computation of quadratic, piecewise quadratic,piecewise linear and polytopic Lyapunov functions. The search for a piecewise linear Lyapunov function is formulated as a linear programming problem, and duality is used to address the non-trivial issue of partition refinements.
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