A generalization of piecewise linear Lyapunov functions

The purpose of this paper is to propose a generalization of piecewise linear Lyapunov functions (PLLFs). In original PLLF candidates, functions are parameterized by hyperplanes, which intersect the stability region and stability conditions are formulated as linear programming problems (LPs) in terms of the parameters inserted by the hyperplanes. The piecewise linear hyperplanes (PLHPs) were introduced to reduce the size of LPs and produce a new class of PLLF candidates; however, applicable systems of this idea were restricted in a certain class of systems. In this paper, this restriction is removed and new PLLF candidates are characterized as the sum of piecewise linear functionals corresponding to PLHPs.