Theoretical Development of Passivity-Preserving Variational Balanced Truncation of Linear Systems

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ABSTRACT0514887Payam HeydariUniversity of California - IrvineThe main of objective of this project is to develop an interdisciplinary program integrating research and education in the area of truncated balanced realization for linear time-invariant (LTI) systems whoseelements are subject to statistical variations. The proposal's research objective is to extend the passivity preserving balanced truncation method to account for the statistical variations of system elements. Inan attempt to reduce the error over the frequency range of interest, the PI's earlier work on spectrally-weighted balanced truncation can also be combined with the proposed variational technique to increase the accuracy of the proposed method across the frequency range of interest. The proposed activity will extend the capabilities of the model-order reduction of LTI systems using balanced truncation in severalsignificant directions, such as guaranteeing passivity and accounting for the statistical variation of the system's elements. Similar to conventional balanced truncation methods, the proposed algorithm providea provable error-bound for the reduced-order system. Integrating the proposed variational balanced truncation method with circuit-level simulation algorithms will provide circuit and system designers apowerful and efficient analytical tool to simulate and optimize large circuits orders of magnitude faster than the Monte-carlo simulation, while retaining the accuracy. The proposed research addresses some ofthe fundamental computational approaches in linear system theory with an application in many areas of engineering, particularly electronic design automation. As a consequence, the interdisciplinary research andeducation, as well as government and industry, will benefit from the proposed work. The PI's close collaboration with local industry will facilitate the dissemination of research results to U.S. high-techcompanies to contribute to the development of new design tools and methodologies for large statistically-varying linear systems. The capability of simulating large circuits while accounting for theemerging problem of process variability will make it possible to carry out statistical simulation with far better accuracy, a capability that is currently impossible to achieve. This in turn will have an impact onfuture multimedia integrated circuits used in the physical layer of wireless/wireline systems. The proposed educational plan will emphasize the participation of underrepresented groups at the high school,undergraduate, and graduate levels in the integrated research and training programs in the area of circuit analysis and optimization. It will foster long-term academic relationships between ethnic-minoritystudent populations at local high schools, and the scientists, educators, and engineers at the UC-Irvine.