This paper addresses the problem of decentralized robust stabilization and control for a class of uncertain Markov jump parameter systems. Control is via output feedback and knowledge of the discrete Markov state. It is shown that the existence of a solution to a collection of mode-dependent coupled algebraic Riccati equations and inequalities, which depend on certain additional parameters, is both necessary and sufficient for the existence of a robust decentralized switching controller. A guaranteed upper bound on robust performance is also given. To obtain a controller which satisfies this bound, an optimization problem involving rank constrained linear matrix inequalities is introduced, and a numerical approach for solving this problem is presented. To demonstrate the efficacy of the proposed approach, an example stabilization problem for a power system comprising three generators and one on-load tap changing transformer is considered.

Abstract-This paper presents a Newton-like algorithm for solving systems of rank constrained linear matrix inequalities. Though local quadratic convergence of the algorithm is not a priori guaranteed or observed in all cases, numerical experiments, including application to an output feedback stabilization problem, show the effectiveness of the algorithm.

Abstract. Presented here are two related numerical methods, one for the inverse eigenvalue problem for nonnegative or stochastic matrices and another for the inverse eigenvalue problem for symmetric nonnegative matrices. The methods are iterative in nature and utilize alternating projection ideas. For the algorithm for the symmetric problem, the main computational component of each iteration is an eigenvalue-eigenvector decomposition, while for the other algorithm, it is a Schur matrix decomposition. Convergence properties of the algorithms are investigated and numerical results are also presented. While the paper deals with two specific types of inverse eigenvalue problems, the ideas presented here should be applicable to many other inverse eigenvalue problems, including those involving nonsymmetric matrices.Key words. inverse eigenvalue problem, nonnegative matrices, stochastic matrices, alternating projections, Schur's decomposition AMS subject classifications. 15A51, 65F18DOI. 10.1137/050634529 1. Introduction. A real n × n matrix is said to be nonnegative if each of its entries is nonnegative.The nonnegative inverse eigenvalue problem (NIEP) is the following: given a list of n complex numbers λ = {λ 1 , . . . , λ n }, find a nonnegative n × n matrix with eigenvalues λ (if such a matrix exists).A related problem is the symmetric nonnegative inverse eigenvalue problem (SNIEP): given a list of n real numbers λ = {λ 1 , . . . , λ n }, find a symmetric nonnegative n × n matrix with eigenvalues λ (if such a matrix exists)1 . Finding necessary and sufficient conditions for a list λ to be realizable as the eigenvalues of a nonnegative matrix has been a challenging area of research for over fifty years, and this problem is still unsolved [12]. As noted in [6, section 6], while various necessary or sufficient conditions exist, the necessary conditions are usually too general while the sufficient conditions are too specific. Under a few special sufficient conditions, a nonnegative matrix with the desired spectrum can be constructed; however, in general, proofs of sufficient conditions are nonconstructive. Two sufficient conditions that are constructive and not restricted to small n are, respectively, given in [20], for the SNIEP, and [21], for the NIEP with real λ. (See also [19] for an extension of the results of the latter paper.) A good overview of known results relating to necessary or sufficient conditions can be found in the recent survey paper [12] and general background material on nonnegative matrices, including inverse eigenvalue problems and applications, can be found in the texts [2] and [18]. We also mention the recent paper [9], which can be used to help determine whether a given list λ may be realizable as the eigenvalues of a nonnegative matrix. http://www.siam.org/journals/simax/28-1/63452.html † Research School of Information Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia (robert.orsi@anu.edu.au).1 The NIEP and SNIEP are different problems even if λ is restrict...

Abstract-In this paper, we consider signals consisting of a finite though unknown number of periodic time-interleaved pulse trains. For such signals, we present a novel approach for determining both the number of pulse trains present and the frequency of each pulse train. Our approach requires only the time of arrival data of each pulse. It is robust to noisy time of arrival data and missing pulses and, above all, is very computationally efficient. If N is the number of pulses being processed, the computation required is of the order of N log N.Index Terms-Pulse train analysis.

Abstract-This paper presents two closely related algorithms for the problem of pole placement via static output feedback. The algorithms are based on two different trust region methods and utilize the derivatives of the closed loop poles. Extensive numerical experiments show the effectiveness of the algorithms in practice though convergence to a solution is not guaranteed for either algorithm. While desired poles must be distinct, strategies for dealing with repeated poles are also presented.Index Terms-Pole placement, static output feedback, trust region method, Newton's method, Levenberg-Marquardt method, eigenvalue derivatives.