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Several problems arising in control system analysis and design, such as reduced order controller synthesis , involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) constraints. Except in some special cases, solving this rank minimization problem (globally) is very difficult. One simple and surprisingly effective… (More)

We present a heuristic for minimizing the rank of a positive semidefinite matrix over a convex set. We use the logarithm of the determinant as a smooth approximation for rank, and locally minimize this function to obtain a sequence of trace minimization problems. We then present a lemma that relates the rank of any general matrix to that of a corresponding… (More)

- DATTORRO Mεβοο, Jon Dattorro, +93 authors Joe Zagami
- 2004

We show how Linear Matrix Inequalities (LMIs) can be used to perform local stability and performance analysis of linear systems with saturating elements. This leads to less conservative information on stability regions, disturbance rejection, and L 2-gain than standard global stability and performance analysis. The Circle and Popov criteria are used to… (More)

- Lin Xiao, Mikael Johansson, Haitham A. Hindi, Stephen P. Boyd, Andrea J. Goldsmith
- IEEE Trans. Automat. Contr.
- 2003

We consider a linear system, such as a controller or estimator, in which several signals are transmitted over communication channels with bit rate limitations. We model the effect of bit rate limited wireless channels by conventional uniform quantization, and use a standard white-noise model for quantization errors. We focus on finding the allocation of… (More)

- Jon Dattorro, Chuck Bagnaschi, +28 authors MaryAnn Young
- 2009

We present minimax and stochastic formulations of some linear approximation problems with uncertain data in R n equipped with the Euclidean (l2), Absolute-sum (l1) or Chebyshev (l1) norms. We then show that these problems can be solved using convex optimization. Our results parallel and extend the work of El-Ghaoui and Lebret on robust least squares 3], and… (More)

— This paper studies tracking of a reference path in a networked control system where the controller consists of a central decision maker and an on-site controller, which are connected through a discrete noiseless channel. The reference path is available noncausally to the central decision maker and the on-site controller has access to noisy observations… (More)

The problem of multiobjective H2=H1 optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer 14]. The problem is formulated as a convex semidef-inite program (SDP) using the LMI formulation of the H2 and H1 norms. Suboptimal solutions are computed using-nite dimensional… (More)

— We propose a settlement mechanism for optimally scheduling real time electricity consumption which is suitable for an automated demand response control system. Our proposed settlement mechanism, supply function bidding, is interpreted as a Newton algorithm for optimization problems with decomposable structure, and it is shown to satisfy the second… (More)