Robust stability of discrete systems

The objective of this paper is to show how to choose a Liapunov function to obtain the best and sometimes exact estimates of the degree of exponential stability for linear time-invariant discrete systems. The choice is interesting because it is also shown that it provides the largest robustness bounds on non-linear time-varying perturbations which can be established by either norm-like or quadratic Liapunov functions. By applying the results obtained to large-scale systems, where the role of perturbations is played by the interconnections among the subsystems, the least conservative stability conditions are derived for the overall system which are available in the context of vector Liapunov functions and M-matrices.