Browsing by Subject "Nevanlinna-Pick interpolation"

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Open Access
Sensitivity minimization by stable controllers: an interpolation approach for suboptimal solutions
(IEEE, 2007) Gümüşsoy, S.; Özbay, Hitay
Weighted sensitivity minimization is studied within the framework of strongly stabilizing (stable)H∞controller design for a class of infinite dimensional systems. This problem has been solved by Ganesh and Pearson, [8], for finite dimensional plants using Nevanlinna-Pick interpolation. We extend their technique to a class of unstable time delay systems. Moreover, we illustrate suboptimal solutions, and their robust implementation.
Open Access
Sensitivity reduction by stable controllers for mIMO infinite dimensional systems via the tangential nevanlinna-Pick interpolation
(IEEE, 2014) Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay
We study the problem of finding a stable stabilizing controller that satisfies a desired sensitivity level for an MIMO infinite dimensional system. The systems we consider have finitely many simple transmission zeros in C +, but they are allowed to possess infinitely many poles in C +. We compute both upper and lower bounds of the minimum sensitivity achievable by a stable controller via the tangential Nevanlinna-Pick interpolation. We also obtain stable controllers attaining such an upper bound. To illustrate the results, we discuss a repetitive control system as an application of the proposed method.
Open Access
Stable controllers for robust stabilization of systems with infinitely many unstable poles
(Elsevier, 2013) Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay
This paper studies the problem of robust stabilization by a stable controller for a linear time-invariant single-input single-output infinite dimensional system. We consider a class of plants having finitely many simple unstable zeros but possibly infinitely many unstable poles. First we show that the problem can be reduced to an interpolation-minimization by a unit element. Next, by the modified Nevanlinna-Pick interpolation, we obtain both lower and upper bounds on the multiplicative perturbation under which the plant can be stabilized by a stable controller. In addition, we find stable controllers to provide robust stability. We also present a numerical example to illustrate the results and apply the proposed method to a repetitive control system.
Open Access
Tangential Nevanlinna-Pick interpolation for strong stabilization of MIMO distributed parameter systems
(IEEE, 2012-12) Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay
We study the problem of finding stable controllers that stabilize a multi-input multi-output distributed parameter system while simultaneously reducing the sensitivity of the system. The plants we consider have finitely many unstable transmission zeros, but they can possess infinitely many unstable poles. Using the tangential Nevanlinna-Pick interpolation with boundary conditions, we obtain both upper and lower bounds of the minimum sensitivity that can be achieved by stable controllers. We also derive a method to find stable controllers for sensitivity reduction. In addition, we apply the proposed method to a repetitive control system. © 2012 IEEE.