<tex-math notation="LaTeX">H₂</tex-math> Analysis of LTI Systems via Conversion to Externally Positive Systems

Motivated by recent advances in the study of linear time-invariant (LTI) positive systems, we explore analysis techniques of general, not necessarily positive, LTI systems using positive system theory. Even though a positive system is characterized by its peculiar property that its impulse response is nonnegative, we often deal with nonnegative impulse responses even in general LTI system analysis. A typical example is the computation of the H2norm, where we focus on squared impulse responses. To deal with such products of impulse responses in a systematic fashion, in this paper, we first establish a construction technique of an LTI system whose impulse response is given by the product of impulse responses of two different LTI systems. Then, as the main result, we reduce the H2norm computation problem of a general LTI system into the L∞-induced norm computation problem (or L1problem in short) of a positive system, by which we can derive various formulas for the H2norm computation.