| 1. |
- Baratchart, L., et al.
(författare)
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Minimal symmetric Darlington synthesis
- 2007
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Ingår i: MCSS. Mathematics of Control, Signals and Systems. - : Springer Science and Business Media LLC. - 0932-4194 .- 1435-568X. ; 19:4, s. 283-311
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Tidskriftsartikel (refereegranskat)abstract
- We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I (p)-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-p-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue.
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| 3. |
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| 4. |
- Hansson, Anders, et al.
(författare)
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Continuous-time blind channel deconvolution using Laguerre shifts
- 2000
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Ingår i: Mathematics of Control, Signals, and Systems. - 0932-4194 .- 1435-568X. ; 13:4, s. 333-346
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Tidskriftsartikel (refereegranskat)abstract
- The objective of this paper is to study the problem of continuous-time blind deconvolution of a pulse amplitude modulated signal propagated over an unknown channel and perturbed by additive noise. The main idea is to use so-called Laguerre filters to estimate a continuous-time model of the channel. Laguerre-filter-based models can be viewed as an extension of finite-impulse-response (FIR) models to the continuous-time case, and lead to compact and parsimonious linear-in-the-parameters models. Given an estimate of the channel, different symbol estimation techniques are possible. Here, the shift property of Laguerre filters is used to derive a minimum mean square error estimator to recover the transmitted symbols. This is done in a way that closely resembles recent FIR-based schemes for the corresponding discrete-time case. The advantage of this concept is that physical a priori information can be incorporated in the model structure, like the transmitter pulse shape.
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| 5. |
- Jarlebring, Elias, et al.
(författare)
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Model reduction of time-delay systems using position balancing and delay Lyapunov equations
- 2013
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Ingår i: MCSS. Mathematics of Control, Signals and Systems. - : Springer Science and Business Media LLC. - 0932-4194 .- 1435-568X. ; 25:2, s. 147-166
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Tidskriftsartikel (refereegranskat)abstract
- Balanced truncation is a standard and very natural approach to approximate dynamical systems. We present a version of balanced truncation for model order reduction of linear time-delay systems. The procedure is based on a coordinate transformation of the position and preserves the delay structure of the system. We therefore call it (structure-preserving) position balancing. To every position, we associate quantities representing energies for the controllability and observability of the position. We show that these energies can be expressed explicitly in terms of the solutions to corresponding delay Lyapunov equations. Apart from characterizing the energies, we show that one block of the (operator) controllability and observability Gramians in the operator formulation of the time-delay system can also be characterized with the delay Lyapunov equation. The delay Lyapunov equation undergoes a contragredient transformation when we apply the position coordinate transformation and we propose to truncate it in a classical fashion, such that positions which are only weakly connected to the input and the output in the sense of the energy concepts are removed.
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| 6. |
- Wijnbergen, Paul, et al.
(författare)
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Impulse-controllability of system classes of switched differential algebraic equations
- 2024
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Ingår i: MCSS. Mathematics of Control, Signals and Systems. - : Springer Nature. - 0932-4194 .- 1435-568X. ; 36:2, s. 351-380
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, impulse-controllability of system classes containing switched DAEs is studied. We introduce several notions of impulse-controllability of system classes and provide a characterization of strong impulse-controllability of system classes generated by arbitrary switching signals. For a system class generated by switching signals with a fixed-mode sequence, it is shown that either almost all systems are impulse-controllable, or almost all systems are impulse-uncontrollable. Sufficient conditions for all systems in this system class to be impulse-controllable or impulse-uncontrollable are presented. Furthermore, it is observed that even if all systems in a system class are impulse-controllable, knowledge of all the switching times is generally necessary to construct an input that ensures impulse-free solutions. Consequently, it is impossible to design a controller in real time if the switching times in the future are unknown. This phenomenon can be regarded as a causality issue. Therefore, the concept of (quasi-) causal impulse-controllability is introduced, and system classes which are (quasi-) causal are characterized. Finally, necessary and sufficient conditions for a system class to be causal given some dwell-time are stated.
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