Uniform global asymptotic stability for half-linear differential systems with time-varying coefficients

Abstract

The present paper deals with the following system:

where p and p^* are positive numbers satisfying 1/p + 1/p^* = 1, and ϕ_q(z) = |z|^q−2z for q = p or q = p^*. This system is referred to as a half-linear system. We herein establish conditions on time-varying coefficients e(t), f(t), g(t) and h(t) for the zero solution to be uniformly globally asymptotically stable. If (e(t), f(t)) ≡ (h(t), g(t)), then the half-linear system is integrable. We consider two cases: the integrable case (e(t), f(t)) ≡ (h(t), g(t)) and the non-integrable case (e(t), f(t)) ≢ (h(t), g(t)). Finally, some simple examples are presented to illustrate our results.