28,553 research outputs found
Model Reduction of Multi-Dimensional and Uncertain Systems
We present model reduction methods with guaranteed error bounds for systems represented by a Linear Fractional Transformation (LFT) on a repeated scalar uncertainty structure. These reduction methods can be interpreted either as doing state order reduction for multi-dimensionalsystems, or as uncertainty simplification in the case of uncertain systems, and are based on finding solutions to a pair of Linear Matrix Inequalities (LMIs). A related necessary and sufficient condition for the exact reducibility of stable uncertain systems is also presented
Canonical lossless state-space systems: Staircase forms and the Schur algorithm
A new finite atlas of overlapping balanced canonical forms for multivariate
discrete-time lossless systems is presented. The canonical forms have the
property that the controllability matrix is positive upper triangular up to a
suitable permutation of its columns. This is a generalization of a similar
balanced canonical form for continuous-time lossless systems. It is shown that
this atlas is in fact a finite sub-atlas of the infinite atlas of overlapping
balanced canonical forms for lossless systems that is associated with the
tangential Schur algorithm; such canonical forms satisfy certain interpolation
conditions on a corresponding sequence of lossless transfer matrices. The
connection between these balanced canonical forms for lossless systems and the
tangential Schur algorithm for lossless systems is a generalization of the same
connection in the SISO case that was noted before. The results are directly
applicable to obtain a finite sub-atlas of multivariate input-normal canonical
forms for stable linear systems of given fixed order, which is minimal in the
sense that no chart can be left out of the atlas without losing the property
that the atlas covers the manifold
An efficient algorithm for positive realizations
We observe that successive applications of known results from the theory of
positive systems lead to an {\it efficient general algorithm} for positive
realizations of transfer functions. We give two examples to illustrate the
algorithm, one of which complements an earlier result of \cite{large}. Finally,
we improve a lower-bound of \cite{mn2} to indicate that the algorithm is indeed
efficient in general
Finding complex balanced and detailed balanced realizations of chemical reaction networks
Reversibility, weak reversibility and deficiency, detailed and complex
balancing are generally not "encoded" in the kinetic differential equations but
they are realization properties that may imply local or even global asymptotic
stability of the underlying reaction kinetic system when further conditions are
also fulfilled. In this paper, efficient numerical procedures are given for
finding complex balanced or detailed balanced realizations of mass action type
chemical reaction networks or kinetic dynamical systems in the framework of
linear programming. The procedures are illustrated on numerical examples.Comment: submitted to J. Math. Che
A lowerbound on the dimension of positive realizations
A basic phenomenon in positive system theory is that the dimension N of an arbitrary positive
realization of a given transfer function H(z) may be strictly larger than the dimension n of its minimal
realizations. The aim of this brief is to provide a non-trivial lower bound on the value of N under the
assumption that there exists a time instant k0 at which the (always nonnegative) impulse response of
H(z) is 0 but the impulse response becomes strictly positive for all k > k0. Transfer functions with this
property may be regarded as extremal cases in positive system theory
Backward Linear Control Systems on Time Scales
We show how a linear control systems theory for the backward nabla
differential operator on an arbitrary time scale can be obtained via Caputo's
duality. More precisely, we consider linear control systems with outputs
defined with respect to the backward jump operator. Kalman criteria of
controllability and observability, as well as realizability conditions, are
proved.Comment: Submitted November 11, 2009; Revised March 28, 2010; Accepted April
03, 2010; for publication in the International Journal of Control
Quasi maximum likelihood estimation for strongly mixing state space models and multivariate L\'evy-driven CARMA processes
We consider quasi maximum likelihood (QML) estimation for general
non-Gaussian discrete-ime linear state space models and equidistantly observed
multivariate L\'evy-driven continuoustime autoregressive moving average
(MCARMA) processes. In the discrete-time setting, we prove strong consistency
and asymptotic normality of the QML estimator under standard moment assumptions
and a strong-mixing condition on the output process of the state space model.
In the second part of the paper, we investigate probabilistic and analytical
properties of equidistantly sampled continuous-time state space models and
apply our results from the discrete-time setting to derive the asymptotic
properties of the QML estimator of discretely recorded MCARMA processes. Under
natural identifiability conditions, the estimators are again consistent and
asymptotically normally distributed for any sampling frequency. We also
demonstrate the practical applicability of our method through a simulation
study and a data example from econometrics
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