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On January 16, ISR Director Eyad Abed (ECE/ISR) gave a seminar talk at the Cymer Center for Control Systems and Dynamics at the University of California, San Diego. He spoke on "System Modes and System States: Their Interplay Revisited."

Dr. Abed was invited to give the lecture by Cymer Center Director Miroslav Krstic. Before moving to UCSD, Krstic was a professor in the University of Maryland's Mechanical Engineering Department and an affiliated faculty member of ISR. Krstic now holds the Harold Sorenson Chair Professorship in the Department of Mechanical and Aerospace Engineering at UCSD.

Here is the abstract of Dr. Abed's talk:

One of the most powerful (and simple) tools in the study of linear systems is the concept of system modes and the circle of ideas known as modal analysis. Although modal analysis is a very well-studied subject, in this lecture we discuss some new insights into an important topic within modal analysis, namely the topic of modal participation factors. Participation factors were introduced three decades ago as a scale-free measure of the degree of participation of system modes in system states, and of the degree of participation of system states in system modes.

Participation factors are a main building block in Selective Modal Analysis, which addresses such issues as model order reduction and placement of actuators and sensors in large-scale systems. In particular, these tools are commonly used in the analysis and design of electric power networks and in the placement of measuring devices and controllers for large power networks. In this work, we take a new approach to the definition of participation factors.

The approach employs defining participations by viewing the system initial condition as either unknown but bounded, or random. In the former case, participation factors are defined by taking a mathematical average over the set of possible initial conditions. In the latter case, participation factors are obtained by taking a mathematical expectation over the assumed random initial condition.

We find that this new approach leads to the common formula for participation factors for measurement of modes in states, but we find that this quantity is of no use in measuring participation of states in modes. An alternative formula is derived for the latter type of modal participation. Implications for the monitoring and control of complex uncertain systems that may be vulnerable to instability are discussed.

January 16, 2009

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