1,130 research outputs found
A Periodic Systems Toolbox for MATLAB
The recently developed Periodic Systems Toolbox for MATLAB is described. The basic approach to develop this toolbox was to exploit the powerful object manipulation features of MATLAB via flexible andfunctionally rich high level m-functions, while simultaneously enforcing highly efficient and numerically sound computations via the mex-function technology of MATLAB to solve critical numerical problems.The m-functions based user interfaces ensure user-friendliness in operating with the functions of this toolbox via an object oriented approach to handle periodic system descriptions. The mex-functions are based on Fortran implementations of recently developed structure exploiting and structure preserving numerical algorithms for periodic systems which completely avoid forming of lifted representations
On the ADI method for the Sylvester Equation and the optimal- points
The ADI iteration is closely related to the rational Krylov projection
methods for constructing low rank approximations to the solution of Sylvester
equation. In this paper we show that the ADI and rational Krylov approximations
are in fact equivalent when a special choice of shifts are employed in both
methods. We will call these shifts pseudo H2-optimal shifts. These shifts are
also optimal in the sense that for the Lyapunov equation, they yield a residual
which is orthogonal to the rational Krylov projection subspace. Via several
examples, we show that the pseudo H2-optimal shifts consistently yield nearly
optimal low rank approximations to the solutions of the Lyapunov equations
Mini-Workshop: Dimensional Reduction of Large-Scale Systems
[no abstract available
On second-order cone positive systems
Internal positivity offers a computationally cheap certificate for external
(input-output) positivity of a linear time-invariant system. However, the
drawback with this certificate lies in its realization dependency. Firstly,
computing such a realization requires to find a polyhedral cone with a
potentially high number of extremal generators that lifts the dimension of the
state-space representation, significantly. Secondly, not all externally
positive systems posses an internally positive realization. Thirdly, in many
typical applications such as controller design, system identification and model
order reduction, internal positivity is not preserved. To overcome these
drawbacks, we present a tractable sufficient certificate of external positivity
based on second-order cones. This certificate does not require any special
state-space realization: if it succeeds with a possibly non-minimal
realization, then it will do so with any minimal realization. While there exist
systems where this certificate is also necessary, we also demonstrate how to
construct systems, where both second-order and polyhedral cones as well as
other certificates fail. Nonetheless, in contrast to other realization
independent certificates, the present one appears to be favourable in terms of
applicability and conservatism. Three applications are representatively
discussed to underline its potential. We show how the certificate can be used
to find externally positive approximations of nearly externally positive
systems and demonstrated that this may help to reduce system identification
errors. The same algorithm is used then to design state-feedback controllers
that provide closed-loop external positivity, a common approach to avoid over-
and undershooting of the step response. Lastly, we present modifications to
generalized balanced truncation such that external positivity is preserved
where our certificate applies
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