Model reduction of uncertain systems retaining the uncertainty structure

Model reduction of high order linear-in-parameters discrete-time systems is considered. The main novelty of the paper is that the coefficients of the original system model are assumed to be known only within given intervals, and the coefficients of the derived reduced order model are also obtained in intervals, such that the complex value sets of the uncertain original and reduced models will be optimally close to each other on the unit circle. The issue of inclusion of one value set in another is also addressed in the paper. The meaning of model reduction is defined for linear-in-parameters systems. The algorithm for obtaining the value sets of such systems is derived in the paper. Then, applying a novel approach, the infinity norm of “distance” between two polygons representing the original and the reduced uncertain systems is minimized. A noteworthy point is that by a special definition of this distance the problem is formulated as a linear semi-infinite programming problem with linear constraints, thus reducing significantly the computational complexity. Numerical example is provided.