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Linear quadratic regulators with eigenvalue placement in a specified region. (English) Zbl 0659.93027
A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at $$\pm \pi /2k$$ $$(k=2$$ or 3) from the negative real axis with a sector angle $$\leq \pi /2$$, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. Also, a shifted sector method is presented to optimally place the closed-loop poles of a system in any general sector having a sector angle between $$\pi$$ /2 and $$\pi$$. The optimal pole placement is achieved without explicitly utilizing the eigenvalues of the open-loop system. The design method is mainly based on the solution of a linear matrix Lyapunov equation and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.

##### MSC:
 93B55 Pole and zero placement problems 93C05 Linear systems in control theory 93C35 Multivariable systems, multidimensional control systems 15A18 Eigenvalues, singular values, and eigenvectors 15A24 Matrix equations and identities
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##### References:
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