Lyapunov stabilizability for nonlinear dynamic control systems on time scales

Abstract

In this paper we use an appropriate Lyapunov function and derive sufficient conditions for the nonlinear dynamic control system x Δ (t )= A(t)x(t )+ B(t)u(t )+ f (t,x(t),u(t)) ,t ∈ T on a time scale T to be uniformly stabilizable, uniformly exponentially stabilizable, and h− stabilizable. Here, A : T → R n×n is an n×n matrix