Seminar by Prof. Li Qiu (Hong Kong University of Science and Technology)

Speaker： Prof. Li Qiu
Department of Electronic and Computer Engineering
Hong Kong University of Science and Technology
http://www.ee.ust.hk/~eeqiu/

Title: Spectrahedral Cone-Invariant Realizations of Nonnegative Impulse Responses

Abstract: It is well-known that not all nonnegative impulse responses have nonnegative state-space realizations. Even in the case when a nonnegative realization exists, its order might be excessively high. Here we propose to realize a nonnegative impulse response using a spectrahedral cone-invariant (SCI) state-space system. Spectrahedral cones are the ones defined by homogeneous LMIs and take the cone of nonnegative vectors as a special case. We are able to find minimal SCI realizations for a large family of nonnegative impulse responses. We will also propose some open problems on realizing some remaining nonnegative impulse responses. Through the realization problem we see the power of SCI systems and we speculate a comprehensive theory of SCI systems.

• Prof. Li Qiu