Pole placement in a specified region based on a linear quadratic regulator

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Abstract
A linear optimal quadratic regulator problem (an LQ-problem) is applied to assign all poles of the multivariable continuous-time system in a suitable region of the left-half complex plane. In particular, two design methods based on an LQ-problem for pole assignments in a truncated sector region of the left-half complex plane, which is given as a common area of a half plane Re λ≧-l > 0 and an open sector tan−1|Im λA/Re λ≦½ are proposed. Each design method is given for the cases where 0 ≧ ½π and 0 ≦ ½π respectively. As these two design methods are derived from two basically different ideas, they will prove more useful if each method can be applied according to the demands of the system's dynamical characteristics.

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