The Lyapunov indicator of discrete inclusions. III (Q1116936)

[For part II see the author, Autom. Remote Control 49, No.3, 283-287 (1988; Zbl 0665.93044).] Certain algebraic formulas characterizing the Lyapunov indicator \(\rho\) of a discrete inclusion are presented. For \(\rho <0\) it is shown that the inclusion state space can be embedded in a space of larger dimension in which the cubic norm decreases along any solution of the inclusion that corresponds to the original one. A similar necessary and sufficient condition is derived for the case \(\rho\geq 0\) too. An algorithm which allows to determine the sign of \(\rho\) in a finite number of steps is also formulated.