Weak Exponential Stability for Time-Periodic Differential Inclusions via First Approximation Averaging

Abstract

Abstract. In this work we propose a method to study a weak exponential stability for time-varying differential inclusions applying an averaging procedure to a first approximation. Namely, we show that a weak exponential stability of the averaged first approximation to the differential inclusion implies the weak exponential stability of the original time-varying inclusion. The result is illustrated by an example.Mathematics Subject Classification (2010). Primary 34A60; Secondary 34C29.

Stability and Optimality of Solutions to Differential Inclusions via Averaging Method

“…Recently, Gama & Smirnov, in [38], studied weak exponential stability for time-periodic Lipschitzian differential inclusions. Their approach consists in the application of the averaging method to the first approximation of inclusion (3), allowing the use of easily verifiable sufficient conditions for exponential stability of convex processes from Smirnov [113].…”

“…Another way to treat problem (29)- (31) is to apply the averaging method to system (37) and (38). Set H(t, x, p) = S(F (t, x), p).…”