Computation of state realizations for control systems described by a class of linear differential-algebraic equations

Control systems described in terms of a class of linear differential-algebraic equations are introduced. Under appropriate relative degree assumptions, a computational procedure for obtaining an equivalent state realization is developed using a singular value decomposition. Properties such as stabil...

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Bibliographic Details
Published in:International journal of control 1992-06, Vol.55 (6), p.1425-1441
Main Authors: KRISHNAN, HARIHARAN, HARRIS McCLAMROCH, N.
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control system analysis
Control theory. Systems
Exact sciences and technology
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Summary:Control systems described in terms of a class of linear differential-algebraic equations are introduced. Under appropriate relative degree assumptions, a computational procedure for obtaining an equivalent state realization is developed using a singular value decomposition. Properties such as stability, controllability, observability, etc, for the differential-algebraic system may be studied directly from the state realization. For linear constrained hamiltonian systems, it is shown that the procedure provides a state realization in which the hamiltonian structure is preserved. Similar results are obtained for constrained gradient systems. Control of systems described by this class of differential-algebraic equations, using a transformation to obtain a state realization, completely avoids the need for any new control theoretic machinery.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179208934292