NDLI: $${{\mathcal H}_{\infty}}$$ control of linear multidimensional discrete systems

Content Provider	Springer Nature Link
Author	Feng, Zhi Yong Wu, Qinghe Xu, Li
Copyright Year	2011
Abstract	This paper presents a comprehensive investigation on the $${{\mathcal H}_{\infty}}$$ control problem of linear multidimensional (nD) discrete systems described by the nD Roesser (local) state-space model. A Bounded Real Lemma consisting of a series of conditions is first established for general nD systems. The proposed nD conditions directly reduce to their 1D counterparts when n = 1, and besides several sufficient conditions which include the existing 2D results as special cases, some necessary and sufficient conditions are also shown to explore further insights to the considered problem. By applying a linear matrix inequality (LMI) condition of the nD Bounded Real Lemma, the nD $${{\mathcal H}_{\infty}}$$ control problem is then considered for three kinds of control laws, namely, static state feedback (SSF) control, dynamic output feedback (DOF) control and static output feedback (SOF) control, respectively. The nD $${{\mathcal H}_{\infty}}$$ SSF and DOF control problems are formulated in terms of an LMI and LMIs, respectively, and thus tractable by using any available LMI solvers. In contrast, the solution condition of the nD $${{\mathcal H}_{\infty}}$$ SOF controller is not strictly in terms of LMIs, therefore an iterative algorithm is proposed to solve this nonconvex problem. Finally, numerical examples are presented to demonstrate the application of these different kinds of nD $${{\mathcal H}_{\infty}}$$ control solutions to practical nD processes as well as the effectiveness of the proposed methods.
Starting Page	381
Ending Page	411
Page Count	31
File Format	PDF
ISSN	09236082
Journal	Multidimensional Systems and Signal Processing
Volume Number	23
Issue Number	3
e-ISSN	15730824
Language	English
Publisher	Springer US
Publisher Date	2011-03-08
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multidimensional discrete systems Roesser model Stability Bounded Real Lemma $${{\mathcal H}_{\infty}}$$ control Linear matrix inequality Artificial Intelligence (incl. Robotics) Circuits and Systems Electrical Engineering Signal, Image and Speech Processing
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Signal Processing Information Systems Computer Science Applications Software Hardware and Architecture

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