Stability assessment for linear time-varying discrete-time systems using orthogonal Lyapunov transformations

A method is given for determining point-wise orthogonal Lyapunov transformations for use in stability studies for linear time-varying discrete-time systems. The advantage of such transformations for the non-periodic case over standard Lyapunov transformations is explained. Simple useful sufficient conditions for asymptotic stability and divergence of the original system are given in terms of the transformed system. The application of the results to online stability assessment is demonstrated.