Analysis of continuous-time piecewise linear (PWL) systems based on piecewise
quadratic (PWQ) Lyapunov functions typically requires continuity of these
functions over a partition of the state space. Several conditions for
guaranteeing continuity of PWQ functions over state space partitions can be
found in the literature. In this technical note, we show that these continuity
conditions are equivalent over so-called simplicial conic partitions. A key
element in our proof is a technical lemma, which, in addition to being of
independent interest, plays a crucial role in demonstrating the equivalence of
these conditions. As a consequence, the choice of which condition to impose can
be based solely on practical considerations such as specific application or
numerical aspects, without introducing additional conservatism in the analysis.

Cet article explore les excursions dans le temps et leurs implications.

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