The first ten Chapters of this book dealt exclusively with single input single output systems with parameter uncertainty. We presented methods for robust analysis and synthesis using formulations that exploited properties of polynomials. A major part of the book was influenced by a variant of the Nyquist Theorem which holds for polynomials, that allowed us to determine D-stability from a finite set of Nyquist plot data. This provided the basis of synthesis procedures for D-stabilisation and robust performance. A second approach employed a rectangular polynomial value set overbound which led to conditions for polynomial family stabilization in terms of the simultaneous stabilization of a finite number of polynomials. Since dynamic descriptions and properties of multi input multi output systems are generalizations and extensions of those for SISO systems and the Nyquist Theorem can still be applied, one would expect that our methods can be extended to the multivariable case. In this Chapter we will demonstrate how the Finite Inclusions Theorem can be used in robust analysis and synthesis of multi input multi output systems with parameter uncertainty.
KeywordsController Parameter Polynomial Matrix Multivariable System Noise Attenuation SISO System
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