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The stability version of the Edge Theorem states that a polytope of polynomials is D-stable if and only if its edge polynomials are all D-stable. Unfortunately, this statement is only true for restricted classes of polytopes and restricted classes of stability regions. If either of these restrictions is removed, the theorem will not be valid. In order to remove these constraints, this paper will present...
This paper investigates the use of stable inverses to obtain multi-model controllers for the simultaneous stabilisation of a class of plants. A parametrization in terms of a stable inverse and a stable null space is proposed for all simultaneously stabilising controllers. Then a strictly proper controller design method for a particular simultaneous pole-placement is devised and the controller for...
The conditioning technique is first reviewed as a particular case of Astr??m and Wittenmark's anti-windup method [11]. Then it is reformulated in terms of a "realizable" reference signal. Using this notion, a method to handle limitations on the manipulated variables of a multivariable control system is presented. The basic idea is to introduce a mapping between the space of manipulated variables...
The presence of uncertain parameters in either a state space or frequency domain description of a linear, time-invariant system manifests itself as variations in the coefficients of the characteristic polynomial. If the family of all such polynomials is polytopic in coefficient space, we'll show that the root locations of the entire family can be completely determined by examining only the roots of...
All the available freedom in selecting the closed-loop Jordan block structure associated with deadbeat controllers is described and the parameters associated with this freedom are characterized. It is shown that in general one has freedom in selecting the Jordan block structure as well as the eigenvectors of deadbeat controllers. Although in general the feedback matrix is a nonlinear function of the...
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