Model reduction of linear structured uncertain systems using an error minimization technique

摘要

This paper presents a method for order reduction of linear structured uncertain systems. The four fixed Kharitonov's polynomials associated with the numerators n_s~I(s), n_m~I(s) and denominators d_s~I(s), d_m~I(s) of the original uncertain system and uncertain reduced model are obtained. By taking all combinations of the n_s~i(s), n_m~i(s) and d_x~j(s), d_m~j(s) for (i,j=1,2,3,4), respectively, we obtain sixteen fixed Kharitonov's systems and sixteen fixed Kharitonov's reduced models. The dominant poles of the sixteen fixed Kharitonov's systems are retained in the corresponding sixteen fixed Kharitonov's reduced models. The numerators of the sixteen fixed Kharitonov's reduced models n_m~(ij)(s) for (i,j=1,2,3,4) are obtained by minimizing the integral square error in step responses between the sixteen fixed Kharitonov's systems H_x~(ij)(s) and the corresponding sixteen fixed Kharitonov's reduced models H_m~(ij)(s). Finally the the upper and lower bounds of the uncertain reduced model c_l~-, c_l~+, d_k~- and d_k~+ for (l=0,1,...,t-1) and (k=1,2,...,r) are obtained from c_l~(ij) and d_l~(ij) for (i,j=1,2,3,4). A numerical example is included in order to indicate how the present method may be applied.