Finite-dimensional Models in Evaluating the H2 Norm of Continuous-time Periodic Systems
نویسندگان
چکیده
Finite-dimensional harmonic models for theH2 norm evaluation of finitedimensional linear continuous-time periodic (FDLCP) systems are derived, which are expressed explicitly through finitely many Fourier coefficients of the system matrices, and thus dispense with the transition matrix knowledge of any FDLCP models, as opposed to most existing methods in the literature. This paper also shows that the skewand square-truncated counterparts to the harmonic state operator are invertible in a class of stable FDLCP systems. This invertibility fact, together with the 2-regularized determinant technique about Hilbert-Schmidt operators, plays a key role in justifying the multiple-step truncation on the unbounded harmonic state operators of FDLCP systems and establishing rigorous convergence arguments for the proposed H2 norm formulae and the associated finite-dimensional harmonic models. Copyright c © 2005 IFAC
منابع مشابه
Algebraic Characterisation of the H ∞ and H 2 Norms for Linear Continuous - Time Periodic Systems ∗
It is well-known that linear, periodically timevarying, continuous-time systems are formally equivalent to so-called lifted representations that are shift-invariant, but have spatially infinitedimensional inputs and outputs. By shift invariance, corresponding frequency-domain representations can be constructed. Indeed, it makes sense to use the H∞ norm of the associated frequencydomain symbol a...
متن کاملDynamic Pricing with Periodic Review and a Finite set of Prices with Cancellation
In this paper, three dynamic pricing models are developed and analyzed. We assume a limited number of a particular asset is offered for sale over a period of time. This asset is perishable and can be an inventory or a manufacturing capacity. During each period, the seller sets a price for this asset. This price is selected from a predetermined discrete set. The maximum amount which a customer i...
متن کاملStatistical Analysis of Stable Fdlcp Systems Described by Higher Order Differential Equations
The paper investigates the response of stable finite dimensional linear continuous-time periodic (FDLCP) systems to white noise input. The FDLCP system is described by differential equations of higher order. Closed formulae for calculating the matrix variance of the output, as well as the mean variance and the H2-norm of the system are derived on basis of the parametric transfer matrix. These f...
متن کاملFinite Dimensional Generating Spaces of Quasi-Norm Family
In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.
متن کاملEntropy operator for continuous dynamical systems of finite topological entropy
In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.
متن کامل