On computing minimal realizations of periodic descriptor systems

Abstract: We propose computationally efficient and numerically reliable algorithms to compute minimal realizations of periodic descriptor systems. The main computational tool employed for the structural analysis of periodic descriptor systems (i.e., reachability and observability) is the orthogonal reduction of periodic matrix pairs to Kronecker-like forms. Specializations of a general reduction algortithm are employed for particular type of systems. One of the proposed minimal realization transformations for which the backward numerical stability can be proved

Quasinormal modes of Kerr-Newman black holes: coupling of electromagnetic and gravitational perturbations

We compute numerically the quasinormal modes of Kerr-Newman black holes in the scalar case, for which the perturbation equations are separable. Then we study different approximations to decouple electromagnetic and gravitational perturbations of the Kerr-Newman metric, computing the corresponding quasinormal modes. Our results suggest that the Teukolsky-like equation derived by Dudley and Finley gives a good approximation to the dynamics of a rotating charged black hole for Q<M/2. Though insufficient to deal with Kerr-Newman based models of elementary particles, the Dudley-Finley equation should be adequate for astrophysical applications.Comment: 13 pages, 3 figures. Minor changes to match version accepted in Phys. Rev.

A Markovian jump system approach for the estimation and adaptive diagnosis of decreased power generation in wind farms

In this study, a Markovian jump model of the power generation system of a wind turbine is proposed and the authors present a closed-loop model-based observer to estimate the faults related to energy losses. The observer is designed through an H∞-based optimisation problem that optimally fixes the trade-off between the observer fault sensitivity and robustness. The fault estimates are then used in data-based decision mechanisms for achieving fault detection and isolation. The performance of the strategy is then ameliorated in a wind farm (WF) level scheme that uses a bank of the aforementioned observers and decision mechanisms. Finally, the proposed approach is tested using a well-known benchmark in the context of WF fault diagnosis

Coupled Potts models: Self-duality and fixed point structure

We consider q-state Potts models coupled by their energy operators. Restricting our study to self-dual couplings, numerical simulations demonstrate the existence of non-trivial fixed points for 2 <= q <= 4. These fixed points were first predicted by perturbative renormalisation group calculations. Accurate values for the central charge and the multiscaling exponents of the spin and energy operators are calculated using a series of novel transfer matrix algorithms employing clusters and loops. These results compare well with those of the perturbative expansion, in the range of parameter values where the latter is valid. The criticality of the fixed-point models is independently verified by examining higher eigenvalues in the even sector, and by demonstrating the existence of scaling laws from Monte Carlo simulations. This might be a first step towards the identification of the conformal field theories describing the critical behaviour of this class of models.Comment: 70 pages; 17 tables and 15 figures in text. Improved numerics; Formula (3.16) and Table 2 correcte

Computation of Zeros of Linear Multivariable Systems

Several algorithms have been proposed in the literature for the computation of the zeros of a linear system described by a state-space model {A, B, C, D}. In this paper we discuss the numerical properties of a new algorithm and compare it with some earlier techniques of computing zeros. The method is a modified version of Silverman&apos;s structure algorithm and is shown to be backward stable in a rigorous sense. The approach is shown to handle both nonsquare and/or degenerate systems. Several numerical examples are also provided

Voltage Stabilization in Microgrids via Quadratic Droop Control

We consider the problem of voltage stability and reactive power balancing in islanded small-scale electrical networks outfitted with DC/AC inverters ("microgrids"). A droop-like voltage feedback controller is proposed which is quadratic in the local voltage magnitude, allowing for the application of circuit-theoretic analysis techniques to the closed-loop system. The operating points of the closed-loop microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide explicit solutions and small-signal stability analyses under several static and dynamic load models. Controller optimality is characterized as follows: we show a one-to-one correspondence between the high-voltage equilibrium of the microgrid under quadratic droop control, and the solution of an optimization problem which minimizes a trade-off between reactive power dissipation and voltage deviations. Power sharing performance of the controller is characterized as a function of the controller gains, network topology, and parameters. Perhaps surprisingly, proportional sharing of the total load between inverters is achieved in the low-gain limit, independent of the circuit topology or reactances. All results hold for arbitrary grid topologies, with arbitrary numbers of inverters and loads. Numerical results confirm the robustness of the controller to unmodeled dynamics.Comment: 14 pages, 8 figure

Nonlinear stability analysis of plane Poiseuille flow by normal forms

In the subcritical interval of the Reynolds number 4320\leq R\leq R_c\equiv 5772, the Navier--Stokes equations of the two--dimensional plane Poiseuille flow are approximated by a 22--dimensional Galerkin representation formed from eigenfunctions of the Orr--Sommerfeld equation. The resulting dynamical system is brought into a generalized normal form which is characterized by a disposable parameter controlling the magnitude of denominators of the normal form transformation. As rigorously proved, the generalized normal form decouples into a low--dimensional dominant and a slaved subsystem. {}From the dominant system the critical amplitude is calculated as a function of the Reynolds number. As compared with the Landau method, which works down to R=5300, the phase velocity of the critical mode agrees within 1 per cent; the critical amplitude is reproduced similarly well except close to the critical point, where the maximal error is about 16 per cent. We also examine boundary conditions which partly differ from the usual ones.Comment: latex file; 4 Figures will be sent, on request, by airmail or by fax (e-mail address: rauh at beta.physik.uni-oldenburg.de