Accuracy-enhancing methods for balancing-related frequency-weighted model and controller reduction.
For a given \(n\)th-order original continuous-time-space model \[ {\mathbf G}= (A,B,C,D), \] let \({\mathbf G}_r= (A_r, B_r, C_r, D_r)\) be an \(r\)th-order approximation of the original model \((r< n)\). Thus, the methods for frequency-weighted model reduction try to minimize a weighted approximation error in the \(L\)-infinity norm and involving weights \(W_0\) and \(W_i\) which are suitably chosen to respectively weight the output and input transfer-function matrices. On the other hand, in a controller reduction problem, for a given stabilizing controller of order \(n_c\), say \({\mathbf K}= (A_c, B_c, C_c, D_c)\) one wants to find \({\mathbf K}_r\), an \(r_c\)th-order approximation with the same number of unstable poles as \({\mathbf K}\), such that a similar weighted error is needed to be minimized. Here, the square-root and balancing-free accuracy-enhancing techniques are extended to this kind of frequency-weighted problems. For this purpose, solving reduced-order Lyapunov equations is required by directly computing the grammians in terms of their Cholesky factors.
square-root accuracy-enhancing techniques
scientific article; zbMATH DE number 1963712
scientific article