A contraction mapping preserving balanced reduction scheme and its infinity norm error bounds

A balanced reduction scheme for linear systems, based on the simultaneous diagonalization of the solutions of the dual algebraic Riccatti equations of the bounded real lemma, is introduced. This procedure reduces a bounded stable transfer matrix S(s) (||S||_∞⩽γ) to a lower order stable transfer matrix S_r(s) with the same bound (||S_r||_∞⩽γ), but more importantly as far as the design of feedback systems is concerned, an L^∞-error bound on (S- S_r) is provided. In addition, the same algorithm also provides reduced-order, stable/minimum phase spectra factors for the power spectra γ²I-S*S and γ²l-SS*, together with identifiable L^∞-error bounds