A new result for closed‐loop poles region of LQ‐optimal discrete‐time systems

Abstract

This paper deals with a new result for pole location of linear quadratic (LQ) optimal discrete-time systems. In this paper a new region in which the closed-loop eigenvalues of an LQ-optimal discrete time system are located is determined. It has been shown that this region is bounded by four lines parallel to the real and imaginary axes, creating a square region. This region is symmetric with respect to the real axis of z-plane, but not with respect to the imaginary axis. Inequality constraints, which bound the closed-loop eigenvalues in a discrete-time LQ-optimal system, are also presented via two theorems. These theorems cover all systems except the ones where A is singular and H is positive semidefinite at the same time. The result is also extended to the problem of the prescribed degree of stability for LQ optimal discrete-time systems.