2019 Volume 32 Issue 7 Pages 284-293
This paper is concerned with the analysis of discrete-time LTI systems via construction of associated externally positive systems. Recently, the authors 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 the H2 norm of the original system by means of the closed-form l∞-induced norm characterization of externally positive systems. It is nonetheless true that, for the original system of order n, the order of the resulting externally positive system is n2, incurring a drastic increase in computational burden of computer-aided analysis and synthesis. With this important issue in mind, in this paper, we show that the order can be reduced down to n(n+1)/2 by using the elimination and duplication matrices that are intensively studied by J. R. Magnus in the 80’s. In addition to the computational complexity reduction for the aforementioned H2 analysis, 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.
