On the stability of positive difference equations

Michaël Di Loreto (1) , Jean Jacques Loiseau (2)

1 AMPERE - Ampère
2 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

In this chapter, we are interested with stability of linear continuous-time difference equations. These equations involve delays, which can be non commensurable. Spectrum analysis comes down to the zeros analysis of an exponential polynomial. From previous results on stability dependent or independent of delays, we focus on the particular case of positive difference equations. It is proved that the stability of linear difference equations with positive coefficients is robust with respect to variations of the delays, and are given exponential bounds for the solution.

Domaines: Automatique / Robotique

Michaël Di Loreto, Jean Jacques Loiseau. On the stability of positive difference equations. Time Delay Systems : Methods, Applications and New Trends Lecture Notes in Control and Information Sciences, Springer, pp.19-33, 2012, 978-3-642-25221-1. ⟨10.1007/978-3-642-25221-1_2⟩. ⟨hal-00957316⟩