### Optimization and Systems Theory Seminar

Friday, July 15, 2005, 11.00-12.00, Room 3721, Lindstedtsvägen 25

Hisaya Fujioka

Department of Applied Analysis and Complex Dynamical Systems

Graduate School of Informatics

Kyoto University

Kyoto 606-8501

Japan

IQC analysis for finite-horizon systems

abstract:

We consider the following IQC (integral quadratic constraint) feasibility
problem: For a given symmetrix matrix and a finite-dimensional state-space
system, determine that the system satisfies the time-domain IQC defined by the
symmetric matrix or not. The difference from the standard setup is twofold: (i)
the time-horizon is finite, and (ii) the two point boundary conditions are given
for the system. We encounter this problem in, e.g., robust control of a class of
PWM systems, and robustness analysis of sampled-data feedback systems. We derive
a finite dimensional condition to verify the IQC as a counterpart of the KYP
lemma in the infinite-horizon case. We then consider the related IQC
optimization problem and a cutting plane algorithm is derived, where we generate
cutting hyperplanes by using infeasible parameters.

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