Imperial College London > Talks@ee.imperial > Control and Power Seminars > The Disturbance Decoupling Problem With Stability for Systems over Digraphs: A Stratified Geometric Approach

The Disturbance Decoupling Problem With Stability for Systems over Digraphs: A Stratified Geometric Approach

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Abstract: We consider the Disturbance Decoupling Problem with Stability (DDPS) for switched discrete-time linear systems, where switching occurs within a set of admissible transitions defined via a weighted directed graph. The concept of subspace arrangement, as a collection of linear subspaces, is employed as a main tool for the definition of geometric properties tailored to switched linear systems on digraphs. Stratified geometric concepts are developed as natural extensions of familiar ones in linear systems theory as applicable to the framework of switched discrete-time linear systems. Invariance concepts are specifically characterized when the system is switched from one mode to the next. The consideration of two types of feedback control, namely a mode-dependent piecewise constant control and a graph-based time-varying control, is seen to induce different notions of controlled invariance, leading to strong and weak controlled invariant subspace arrangements, respectively. Sufficient conditions for solvability of DDPS under certain classes of admissible switching signals are expressed in terms of the proposed invariance notions. Conditions for eigenvalue assignment and stabilizability are provided under the assumptions of arbitrary dwell-time and sufficiently large dwell-time switching strategies, respectively. These results specialize previous approaches based on robust controlled invariance, while providing a constructive solution in cases where previous methodologies fail.

Biography: Andrea Serrani received the Ph.D. degree from the University of Ancona, Italy, in 1997, and the D.Sc. degree from Washington University in Saint Louis in 2000. Since 2002, he has been with The Ohio State University, Columbus, Ohio, where he is currently a Professor. His research activity spans the field of control and systems theory, with applications to aerospace and vehicular systems. He is the co-author (with A. Isidori and L. Marconi) of the book Robust Autonomous Guidance—An Internal Model Approach, published by Springer Verlag. Prof. Serrani is a Fulbright Fellow and the recipient of four US Air Force Fellowships. He is currently the Editor-in-Chief for the IEEE Transactions on Control Systems Technology and an Associate Editor for the IEEE CSS and EUCA Conference Editorial Boards, and has served in the past on the editorial boards of Automatica and the International Journal of Robust and Nonlinear Control. He is a member of IEEE , AIAA, and IFAC . He is the Program Chair of the upcoming 2019 American Control Conference.

This talk is part of the Control and Power Seminars series.

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