Error bounds for balanced truncation of linear time-varying systems

In this paper error bounds for truncated balanced linear time-varying systems in discrete time are obtained. The analysis is based on direct calculations with the time-varying observability and controllability Lyapunov inequalities. The obtained bounds in the induced ₂-norm, generalize well-known error-bound formulas for time-invariant systems. The case of time-varying state-space dimension is considered, and this proves to be valuable both for technical and practical reasons. The input-output stability of truncated models is shown to be guaranteed.