Stability for time varying linear dynamic systems on time scales

We study conditions under which the solutions of a time varying linear dynamic system of the form x Δ ( t ) = A ( t ) x ( t ) are stable on certain time scales. We give sufficient conditions for various types of stability, including Lyapunov-type stability criteria and eigenvalue conditions on “slowly varyingʹʹ systems that ensure exponential stability. Finally, perturbations of the unforced system are investigated, and an instability criterion is also developed.