A study on the l1 analysis of discrete-time systems

Abstract

This paper studies computing the l∞-induced norm of multi-input/multi-output (MIMO) linear time-invariant (LTI) discrete-time systems, which is called the l1 analysis problem. Because such a computation involves an infinite-dimensional matrix, this paper employs a truncation idea to approximately deal with the l1 analysis problem. More precisely, this paper develops two methods for computing the l∞-induced norm, in which upper bounds and lower bounds of the l∞-induced norm are derived on the truncated treatment. Furthermore, it is shown that the gaps between the computed upper and lower bounds converge to 0 at an exponential rate of N, where N is the truncation parameter. Finally, a numerical exampled is provided to demonstrate the effectiveness of the developed computation methods. ？ 2017 Institute of Control, Robotics and Systems - ICROS.