کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
697488 890372 2008 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Linear systems theory revisited
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
پیش نمایش صفحه اول مقاله
Linear systems theory revisited
چکیده انگلیسی

This paper investigates and clarifies how different definitions of reachability, observability, controllability, reconstructability and minimality that appear in the control literature, may be equivalent or different, depending on the type of linear system. The differences are caused by (1) whether or not the linear system has state dimensions that vary with time (2) bounds on the time axis of the linear system (3) whether or not the initial state is non-zero and (4) whether or not the system is time invariant. Also (5) time-reversibility of systems plays a role. Discrete-time linear strictly proper systems are considered. A recently published result is used to argue that all the results carry over to continuous time. Out of the investigation two types of definitions emerge. One type applies naturally to systems with constant dimensions while the other applies naturally to systems with variable dimensions. This paper reveals that time-varying (state) dimensions that are allowed to be zero are necessary to obtain equivalence between minimality and (weak) reachability together with observability at the systems level. Besides their theoretical significance the results of this paper are of practical importance for model reduction and control of time-varying discrete-time linear systems because they result in minimal realizations with smaller dimensions that are also computed more easily.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Automatica - Volume 44, Issue 7, July 2008, Pages 1686–1696
نویسندگان
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