On Computing the Worst-Case Peak Gain of Linear Systems

V. Balakrishnan and S. Boyd

Systems and Control Letters, 19:265-269, 1992.
Conference paper appeared in Proceedings IEEE Conference on Decision and Control, 2:2191-2192, 1992.

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 ell_1-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 ell_infty-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 ell_infty-gain of discrete-time systems with diagonal perturbations.