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Discrete-time optimal regulator with closed-loop poles in a prescribed region. (English) Zbl 0641.93030

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
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References:

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