Construction of Externally Positive Systems for Discrete-Time LTI System Analysis

摘要

This paper is concerned with analysis techniques of discrete-time LTI systems via construction of relevant externally positive systems. Recently, the author established a construction method of an externally positive system whose impulse response is given by the square of the original discrete-time LTI SISO system to be analyzed. This externally positive system allows us to characterize theH2norm of the original system by means of thel∞-induced norm characterization of externally positive systems. It is nonetheless true that, for the original system of ordern, the order of the resulting externally positive system isn2and hence this leads to the increase of associated computational burden. With this important issue in mind, in this paper, we show that the order can be reduced down ton(n+ 1)/2 by using the elimination and duplication matrices that are intensively studied by Jan R. Magnus in the 80’s. In addition to the computational complexity reduction for the aforementionedH2analysis, we show that such construction of externally positive systems with reduced order is quite effective in semidefinite-programming-based peak value analysis of impulse responses of general LTI systems.