Abstract
The paper presents a method for order reduction of linear structured uncertain systems. The four fixed Kharitonov's polynomials associated with the numerators n(B)(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(B)(i)(s), n(m)(i)(s) and d(B)(i)(s), d(m)(i)(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 H-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-ai(j)(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(i)(-),c(i)(+),d(k)(-) and d(k)(+) for (l=0,1,...,tau-1) and (k=1,2,...,tau) are obtained from c(l)(ij) and c(l)(ij) for (i, j = i, 2, 3, 4). A numerical example is included in order to indicate how the present method may be applied.