We consider a class of spatially distributed systems with spatially periodic coefficients. Frequency domain methods are used to convert a linear system belonging to this class into a family of infinite-dimensional LTI ones. The frequency and amplitude of the periodic coefficients are then treated as parameters. A perturbation analysis is then performed on the amplitude of the periodicity to fin...

Kalman-Yakubovich-Popov (KYP) Lemma (also frequently called “positive real lemma”) is a major result of the modern linear system theory. It is a collection of statements related to existence and properties of quadratic storage functions for LTI state space models and quadratic supply rates. The KYP Lemma is used in the derivation of H2 and H-Infinity optimal controllers, Hankel optimal reduced ...

this article presents a new subspace-based technique for reducing the noise ofsignals in time-series. in the proposed approach, the signal is initially representedas a data matrix. then using singular value decomposition (svd), noisy datamatrix is divided into signal subspace and noise subspace. in this subspace division,each derivative of the singular values with respect to rank order is used ...

The state feedback H1 control problem for standard discrete-time singularly perturbed systems with polytopic uncertainties is considered. Two methods for designing H1 controllers are given in terms of solutions to a set of linear matrix inequalities, where one of them is with the consideration of improving the upper bound of singular perturbation parameter e. Moreover, a method of evaluating th...

Geometric singular perturbation theory is a useful tool in the analysis of problems with a clear separation in time scales. It uses invariant manifolds in phase space in order to understand the global structure of the phase space or to construct orbits with desired properties. This paper explains and explores geometric singular perturbation theory and its use in (biological) practice. The three...

In this paper, we address the performance limitation issues in estimation problems. Our purpose is to explicitly relate the best achievable estimation errors with simple plant characteristics. In particular, we study performance limitations in achieving four objectives: (1) estimating the output of an LTI system from its version corrupted by a white noise, (2) estimating a Brownian motion from ...

In this paper we show that stability for holomorphic vector bundles are equivalent to the existence of solutions to certain system of Monge Amp ere equations parametrized by a parameter k. We solve this fully nonlinear elliptic system by singular perturbation technique and show that the vanishing of obstructions for the perturbation is given precisely by the stability condition. This can be int...

Linear time-periodic (LTP) dynamical systems frequently appear in the modeling of phenomena related to fluid dynamics, electronic circuits, and structural mechanics via linearization centered around known periodic orbits of nonlinear models. Such LTP systems can reach orders that make repeated simulation or other necessary analysis prohibitive, motivating the need for model reduction. We develo...

In this paper, let A and B be n x p complex tensors = + E. Denote the T-Drazin inverse of by AD. We give a perturbation bound for ||BD-AD||=||AD|| under condition (W). Considering solution singular tensor equation A* b, (b ? R(AD)) at same time. The optimal system equations have been given.