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Corless M.,Purdue University | Shorten R.,Hamilton Institute
Automatica | Year: 2011

Systems and control theory has long been a rich source of problems for the numerical linear algebra community. In many problems, conditions on analytic functions of a complex variable are usually evaluated by solving a special generalized eigenvalue problem. In this paper we develop a general framework for studying such problems. We show that for these problems, solutions can be obtained by either solving a generalized eigenvalue problem, or by solving an equivalent eigenvalue problem. A consequence of this observation is that these problems can always be solved by finding the eigenvalues of a Hamiltonian (or discrete-time counterpart) matrix, even in cases where an associated Hamiltonian matrix, cannot (normally) be defined. We also derive a number of new compact tests for determining whether or not a transfer function matrix is strictly positive real. These tests, which are of independent interest due to the fact that many problems can be recast as SPR problems, are defined even in the case when the matrix D+D* is singular, and can be formulated without requiring inversion of the system matrix A. © 2010 Elsevier Ltd. All rights reserved. Source

Middleton R.H.,Hamilton Institute | Braslavsky J.H.,University of Newcastle
IEEE Transactions on Automatic Control | Year: 2010

This paper gives sufficient conditions for string instability in an array of linear time-invariant autonomous vehicles with communication constraints. The vehicles are controlled autonomously and are subject to a rigid or semi-rigid formation policy. The individual controllers are assumed to have a limited range of forward and backward communication with other vehicles. Sufficient conditions are given that imply a lower bound on the peak of the frequency response magnitude of the transfer function mapping a disturbance to the leading vehicle to a vehicle in the chain. This lower bound quantifies the effect of spacing separation policy, intervehicle communication policy, and vehicle settling response performance. These results extend earlier works to give a unified treatment of heterogeneous, non-nearest neighbor communication and semi-rigid one-dimensional formation control. © 2006 IEEE. Source

Zappavigna A.,Polytechnic of Milan | Charalambous T.,University of Cyprus | Knorn F.,Hamilton Institute
Automatica | Year: 2012

In this note we prove the unconditional stability of the FoschiniMiljanic algorithm. Our results show that the FoschiniMiljanic algorithm is unconditionally stable (convergent) even in the presence of bounded time-varying communication delays, and in the presence of topology changes. The implication of our results may be important for the design of Code Division Multiple Access (CDMA) based wireless networks. © 2011 Elsevier Ltd. All rights reserved. Source

Corless M.,Purdue University | Shorten R.,Hamilton Institute
IEEE Transactions on Automatic Control | Year: 2010

We present conditions which are necessary and sufficient for a transfer function (or transfer function matrix) to be strictly positive real. A counter-example is given to illustrate that the conditions presented here differ from those previously presented in the literature. The proof of our results differs from previous related proofs in that it only uses properties of analytic functions and matrices and does not require state-space realizations. Also, the results are not restricted to rational transfer functions with real coefficients. © 2010 IEEE. Source

Subramanian V.G.,Hamilton Institute | Berry R.A.,Northwestern University | Agrawal R.,Motorola Inc.
IEEE Transactions on Information Theory | Year: 2010

In this paper, the scheduling and resource allocation problem for the downlink in a code-division multiple access (CDMA)-based wireless network is considered. The problem is to select a subset of the users for transmission and for each of the users selected, to choose the modulation and coding scheme, transmission power, and number of codes used. We refer to this combination as the physical layer operating point (PLOP). Each PLOP consumes different amounts of code and power resources. The resource allocation task is to pick the optimal PLOP taking into account both system-wide and individual user resource constraints that can arise in a practical system. This problem is tackled as part of a utility maximization problem framed in earlier papers that includes both scheduling and resource allocation. In this setting, the problem reduces to maximizing the weighted throughput over the state-dependent downlink capacity region while taking into account the system-wide and individual user constraints. This problem is studied for the downlink of a Gaussian broadcast channel with orthogonal CDMA transmissions. This results in a tractable convex optimization problem. A dual formulation is used to obtain several key structural properties. By exploiting this structure, algorithms are developed to find the optimal solution with geometric convergence. © 2010 IEEE. Source

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