Inclusion Principle for Descriptor Systems

• Published in: IEEE transactions on automatic control Vol. 54; no. 1; pp. 3 - 18
• Main Authors: Delin Chu, Ohta, Y., Siljak, D.D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-01-2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Biological system modeling; Computer science; control theory; systems; Concurrent computing; Constraint theory; Contractibility; contractions; Control design; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Controllability; controllability at infinity; descriptor systems; Design engineering; Dynamical systems; Dynamics; Exact sciences and technology; expansions; H infinity control; inclusion principle; Inclusions; Initial conditions; Law; Mathematical analysis; Modelling and identification; Optimal control; Power system modeling; Vehicle dynamics; Contractibility; Descriptor system; inclusion principle; Information system; descriptor systems; Control program; controllability at infinity; Control synthesis; Controllability; Dynamical system; expansions; contractions
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2008.2009482

The purpose of this paper is to propose an expansion-contraction framework for linear constant descriptor systems within the inclusion principle for dynamic systems. Our primary objective is to provide an explicit characterization of the expansion process whereby a given descriptor system is expanded into the larger space where all its solutions are reproducible by the expanded descriptor system if appropriate initial conditions are selected. When a control law is formulated in the expanded space, the proposed characterizations provide contractibility conditions for implementation of the control law in the original system. A full freedom is provided for selecting appropriate matrices in the proposed expansion-contraction control scheme. In particular, the derived theoretical framework serves as a flexible environment for expansion-contraction control design of descriptor systems under overlapping information structure constraints.