On stability robustness with respect to LTV uncertainties

It is shown that the well-known (D,G)-scaling upper bound of the structured singular value is a nonconservative test for robust stability with respect to certain linear time-varying uncertaintie

A New Distributed Localization Method for Sensor Networks

This paper studies the problem of determining the sensor locations in a large sensor network using relative distance (range) measurements only. Our work follows from a seminal paper by Khan et al. [1] where a distributed algorithm, known as DILOC, for sensor localization is given using the barycentric coordinate. A main limitation of the DILOC algorithm is that all sensor nodes must be inside the convex hull of the anchor nodes. In this paper, we consider a general sensor network without the convex hull assumption, which incurs challenges in determining the sign pattern of the barycentric coordinate. A criterion is developed to address this issue based on available distance measurements. Also, a new distributed algorithm is proposed to guarantee the asymptotic localization of all localizable sensor nodes

Generalizations of the Nevanlinna-Pick interpolation problem

Abstract — This paper aims at generalizing the well-known Nevanlinna-Pick interpolation problem by considering additional constraints. The first type of constraints we consider requires the interpolation function to be of a given degree. Several results are provided for different degree constraints. These results offer feasibility tests via linear matrix inequalities. We have identified a number of degree constraints for which the feasibility tests are exact. For other degree constraints, we offer a relaxation scheme for checking the feasibility. The second type of constraints we study is about spectral zero assignment, which demands the zeros of the spectral factorization of the interpolation function to be at given locations. This problem can be solved using an iterative algorithm by Byrnes, Georgiou and Linquist. However, we provide a much faster iterative algorithm for this problem, although a proof of convergence is yet to be offered. I

Distributed Kalman Estimation with Decoupled Local Filters

We study a distributed Kalman filtering problem in which a number of nodes cooperate without central coordination to estimate a common state based on local measurements and data received from neighbors. This is typically done by running a local filter at each node using information obtained through some procedure for fusing data across the network. A common problem with existing methods is that the outcome of local filters at each time step depends on the data fused at the previous step. We propose an alternative approach to eliminate this error propagation. The proposed local filters are guaranteed to be stable under some mild conditions on certain global structural data, and their fusion yields the centralized Kalman estimate. The main feature of the new approach is that fusion errors introduced at a given time step do not carry over to subsequent steps. This offers advantages in many situations including when a global estimate in only needed at a rate slower than that of measurements or when there are network interruptions. If the global structural data can be fused correctly asymptotically, the stability of local filters is equivalent to that of the centralized Kalman filter. Otherwise, we provide conditions to guarantee stability and bound the resulting estimation error. Numerical experiments are given to show the advantage of our method over other existing alternatives