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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.

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
Full Text: DOI
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