Uniform exponential stability for families of linear time-varying systems

We present sufficient conditions for uniform exponential stability of families of linear time varying (LTV) systems. That is, LTV systems characterized by certain parameters. Our conditions are in the form of classical concepts in adaptive control, such as persistency of excitation. However, our proofs are based on modern tools which can be interpreted as an “integral” version of Lyapunov theorems; rather than on the concept of uniform complete observability which is most common in the literature. Uniformity is established in both, the initial conditions of the system, and the parameter which characterizes each system of the “family”