Model Reduction of Linear Structured Uncertain Systems Using Chebyshev Polynomial Techniques

This paper presents a method of reduction for linear structured uncertain systems over a desired frequency interval. The four fixed Kharitonov´s polynomials associated with the numerators and denominators of the original uncertain system and uncertain reduced model are obtained. The stability equation method is used to preserve the stability of the sixteen fixed Kharitonov´s systems and original uncertain system by first determining the denominator coefficients of the sixteen fixed Kharitonov´s reduced models and uncertain reduced model respectively. The numerators of the sixteen fixed Kharitonov´s reduced models are determined by matching the first (r-1) terms of Chebyshev polynomial series expansions of fixed systems with that of the corresponding Chebyshev polynomial series expansions of fixed models. Finally the lower and upper bounds of the uncertain reduced model are found from the coefficients of the sixteen fixed Kharitonov´s reduced models. A numerical example is provided to demonstrate various aspects of theoretical results