Interpolatory methods for H∞\mathcal{H}_\infty model reduction of multi-input/multi-output systems

We develop here a computationally effective approach for producing high-quality $\mathcal{H}_\infty$-approximations to large scale linear dynamical systems having multiple inputs and multiple outputs (MIMO). We extend an approach for $\mathcal{H}_\infty$ model reduction introduced by Flagg, Beattie, and Gugercin for the single-input/single-output (SISO) setting, which combined ideas originating in interpolatory $\mathcal{H}_2$-optimal model reduction with complex Chebyshev approximation. Retaining this framework, our approach to the MIMO problem has its principal computational cost dominated by (sparse) linear solves, and so it can remain an effective strategy in many large-scale settings. We are able to avoid computationally demanding $\mathcal{H}_\infty$ norm calculations that are normally required to monitor progress within each optimization cycle through the use of "data-driven" rational approximations that are built upon previously computed function samples. Numerical examples are included that illustrate our approach. We produce high fidelity reduced models having consistently better $\mathcal{H}_\infty$ performance than models produced via balanced truncation; these models often are as good as (and occasionally better than) models produced using optimal Hankel norm approximation as well. In all cases considered, the method described here produces reduced models at far lower cost than is possible with either balanced truncation or optimal Hankel norm approximation

New efficient frequency domain algorithm for H∞approximation with applications to controller reduction

New frequency domain computational schemes for the weighted and unweighted H∞ norm system approximation problems are introduced. The schemes are applicable in both continuous and discrete-time cases. The new algorithm is used to obtain reduced order controllers for a well known control proble

New Efficient Frequency Domain Algorithm For H-Infinity Approximation

New frequency domain computational schemes for the weighted and unweighted H infinity norm system approximation problems are introduced. The schemes are applicable in both continuous and discrete-time cases. The new algorithm is used to obtain reduced order controllers for a well known control problem

Simultaneous stabilization of MIMO systems via robustly stabilizinga central plant

In this note, a new formulation and solution to the simultaneous stabilization problem (SSP) is given. The new method is based on finding a central plant from a set of plants to be simultaneously stabilized. The theory of robust stabilization can then be applied to the central plant with a bounded perturbation, which encapsulates the plants to be stabilized, in order to solve the SS

An optimal broadcasting protocol for mobile video-on-demand

Pulse-echo reflection techniques are used for ultrasonic flaw detection in most commercial instruments [1,2]. The ultrasonic wave, generated by a piezoelectric transducer coupled to the test specimen, propagates through the material and part of its energy is reflected when it encounters a non-homogeneity or discontinuity in its path, while the remainder is reflected by the back surface of the test specimen. The flaw echo contains information regarding the material discontinuity that the ultrasonic wave has encountered in its path