Stability of control systems and graphs of linear systems. (English) Zbl 0747.93062

Ober, R. J.; Sefton, J. A.

Syst. Control Lett. 17, No. 4, 265-280 (1991).

Summary: New conditions for internal stability of a closed-loop control system are given in terms of the graphs of the multiplication operators induced by the transfer functions of the plant and the controller. These conditions can be given a geometrical interpretation. This relates closed-loop stability to the minimal angle between the graph space associated with the system and the graph space associated with the controller. The maximally stabilizing controller is defined as the controller that maximizes the minimum angle between the graph space associated with the controller. It is shown that this controller can be calculated as a Nehari extension of the coprime factors of the system.

MSC:

93D05	Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C05	Linear systems in control theory

Keywords:

internal stability; closed-loop control system; maximally stabilizing controller

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