A Study on the l(1) Analysis of Discrete-Time Systems

Abstract

This paper studies computing the l(infinity)-induced norm of multi-input/multi-output (MIMO) linear time-invariant (LTI) discrete-time systems, which is called the l(1) analysis problem. Because such a computation involves an infinite-dimensional matrix, this paper employs a truncation idea to approximately deal with the l(1) analysis problem. More precisely, this paper develops two methods for computing the l(infinity)-induced norm, in which upper bounds and lower bounds of the l(infinity)-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.