Achim Ilchmann

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Tracking of a reference signal (assumed bounded with essentially bounded derivative) is considered in the context of a class Σρ of multi-input, multi-output dynamical systems, modelled by functional differential equations, affine in the control and satisfying the following structural assumptions: (i) arbitrary – but known – relative degree ρ ≥ 1, (ii) the(More)
We control a two mass system with uncertain parameter values, encompassing friction and hysteretic effects, modelled as a functional differential equation. As opposed to control strategies invoking identification mechanisms or neural networks, we propose controllers relying on structural system properties only. Output behaviour with prespecified accuracy is(More)
Tracking of a reference signal (assumed bounded with essentially bounded derivative) is considered in a context of a class of nonlinear systems, with output y, described by functional differential equations (a generalization of the class of linear minimum-phase systems with positive high-frequency gain). The primary control objective is tracking with(More)
Tracking of reference signals yref(·) by the output y(·) of linear (as well as a considerably large class of nonlinear) single-input, single-output system is considered. The system is assumed to have strict relative degree two with (“weak”) stable zero dynamics. The control objective is tracking of the error e = y− yref and its derivative ė within two(More)
In this paper we study a particular class of -node recurrent neural networks (RNN's). In the 3-node case we use monotone dynamical systems theory to show, for a well-defined set of parameters, that, generically, every orbit of the RNN is asymptotic to a periodic orbit. Then we investigate whether RNN's of this class can adapt their internal parameters so as(More)
In the sequel to [A. Ilchmann and V. Mehrmann, SIAM J. Control Optim., 44 (2005), pp. 1725–1747], we discuss a behavioral approach for linear, time-varying, differential algebraic (descriptor) systems with real analytic coefficients. The analysis is “almost global” in the sense that the analysis is not restricted to an interval I ⊂ R but is allowed for the(More)
Tracking—by the system output—of a reference signal (assumed bounded with essentially bounded derivative) is considered in the context of linear -input, -output systems subject to input saturation. The system is assumed to have strict relative degree one with stable zero dynamics. Prespecified is a performance funnel, within which the tracking error is(More)
Tracking of a reference signal (assumed bounded with essentially bounded derivative) is considered for multi-input, multi-output linear systems satisfying the following structural assumptions: (i) arbitrary – but known – relative degree, (ii) the “high-frequency gain” matrix is sign definite – but of unknown sign, (iii) exponentially stable zero dynamics.(More)
For linear, square, multi-input–multi-output, minimum-phase, relative-degree one or two systems, proportional output feedback controllers are studied. In particular, we show that derivative feedback can be replaced by delay feedback, essentially an Euler approximation of the derivative, if the delay is su3ciently small. Stability regions are determined and(More)