Fujinaka, Toru; Katayama, Tohru Discrete-time optimal regulator with closed-loop poles in a prescribed region. (English) Zbl 0641.93030 Int. J. Control 47, No. 5, 1307-1321 (1988). This paper is concerned with the problem designing discrete-time optimal control systems with closed-loop poles in a prescribed region of stability. First, by utilizing the property of the Riccati equation with Q being zero, we develop a method for allocating poles in a disc with centre at the origin of the complex plane and with radius less than 1. Secondly, we deal with pole placement in a disc which is in the unit disc and also contacts the point \(1+j0\) of the complex plane. To this end, a bilinear transformation and continuous-time regulator results are employed. In each case, the radius of the disc can be specified as a design parameter, and the weighting matrices of the performance index are obtained to fulful the desired pole allocations. The design procedures are also illustrated by numerical examples. MSC: 93B55 Pole and zero placement problems 93C05 Linear systems in control theory 93C55 Discrete-time control/observation systems 15A24 Matrix equations and identities 93B50 Synthesis problems 93B17 Transformations Keywords:discrete-time optimal control; closed-loop poles; prescribed region of stability; Riccati equation; pole placement; bilinear transformation PDFBibTeX XMLCite \textit{T. Fujinaka} and \textit{T. Katayama}, Int. J. Control 47, No. 5, 1307--1321 (1988; Zbl 0641.93030) Full Text: DOI References: [1] DOI: 10.1080/00207178408933307 · Zbl 0547.93033 · doi:10.1080/00207178408933307 [2] ANDERSON B. D. O., Linear Optimal Control (1971) · Zbl 0321.49001 [3] KAILATH T., Linear Systems (1980) [4] DOI: 10.1080/0020718508961156 · Zbl 0566.93041 · doi:10.1080/0020718508961156 [5] DOI: 10.1016/0005-1098(83)90011-0 · Zbl 0524.93028 · doi:10.1016/0005-1098(83)90011-0 [6] DOI: 10.1109/TAC.1986.1104110 · Zbl 0584.93010 · doi:10.1109/TAC.1986.1104110 [7] KWAKERNAAK H., Linear Optimal Control Systems (1972) · Zbl 0276.93001 [8] DOI: 10.1109/TAC.1979.1102178 · Zbl 0424.65013 · doi:10.1109/TAC.1979.1102178 [9] DOI: 10.1109/TAC.1980.1102434 · Zbl 0456.49010 · doi:10.1109/TAC.1980.1102434 [10] DOI: 10.1080/00207177208932136 · Zbl 0225.49026 · doi:10.1080/00207177208932136 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.