On Computing the Worst-Case Peak Gain of Linear Systems
Systems and Control Letters, 19:265-269, 1992.
Conference paper appeared in Proceedings IEEE Conference on Decision and
Control, 2:2191-2192, 1992.
CDC paper: wc_ell_one_cdc.pdf XXX
Based on the bounds in the paper by Boyd and Doyle (Comparison of peak
and RMS gains for discrete-time systems, Systems and Control Letters, 9:1-6),
we present simple upper and lower bounds for the 
-norm of the tail
of the impulse response of finite-dimensional discrete-time linear
time-invariant systems. Using these bounds, we may in turn compute the
-gain of these systems to any desired accuracy. By combining these
bounds with results from Khammash and Pearson (Performance robustness of
discrete-time systems with structured uncertainty, IEEE T-AC 36:398-412),
we derive upper and lower bounds for the worst-case
-gain of discrete-time systems with diagonal perturbations.