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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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