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A Function Space Approach to SampledData Control Systems And Tracking Problems
 IEEE Transactions on Automatic Control
, 1994
"... This paper presents a new framework for hybrid sampleddata control systems. ..."
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Cited by 11 (4 self)
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This paper presents a new framework for hybrid sampleddata control systems.
Learning Control and Related Problems in InfiniteDimensional Systems
 in Essays on Control, eds. H.L.Trentelman and J.C. Willems, Birkhauser
, 1993
"... The basic features of a special type of learning control scheme, currently known as repetitive control are reviewed. It is seen that this control scheme also induces varied interesting theoretical problems particularly those related to infinitedimensional systems. They include such problems ..."
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Cited by 6 (1 self)
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The basic features of a special type of learning control scheme, currently known as repetitive control are reviewed. It is seen that this control scheme also induces varied interesting theoretical problems particularly those related to infinitedimensional systems. They include such problems as the internal model principle, minimal representation of transfer functions, fractional representations, stability characterizations, correspondence of internal and external stability, etc. This article intends to give a comprehensive overview of the repetitive control scheme as well as the discussion of these related theoretical problems for infinitedimensional systems.
Equivalence of Internal and External Stability for a Class of Distributed Systems
, 1990
"... It is well known that for infinitedimensional systems, exponential stability is not necessarily determined by the location of spectrum. ..."
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Cited by 6 (4 self)
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It is well known that for infinitedimensional systems, exponential stability is not necessarily determined by the location of spectrum.
An Introduction to Internal Stabilization of InfiniteDimensional Linear Systems
"... In these notes, we give a short introduction to the fractional representation approach to analysis and synthesis problems [12], [14], [17], [28], [29], [50], [71], [77], [78]. In particular, using algebraic analysis (commutative algebra, module theory, homological algebra, Banach algebras), we shall ..."
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Cited by 3 (1 self)
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In these notes, we give a short introduction to the fractional representation approach to analysis and synthesis problems [12], [14], [17], [28], [29], [50], [71], [77], [78]. In particular, using algebraic analysis (commutative algebra, module theory, homological algebra, Banach algebras), we shall give necessary and sufficient conditions for a plant to be internally stabilizable or to admit (weakly) left/right/doubly coprime factorizations. Moreover, we shall explicitely characterize all the rings A of SISO stable plants such that every plant defined by means of a transfer matrix with entries in the quotient field K = Q(A) of A satisfies one of the previous properties (e.g. internal stabilization, (weakly) doubly coprime factorizations). Using the previous results, we shall show how to parametrize all stabilizing controllers of an internally stabilizable plants which does not necessarily admits a doubly coprime factorization. Finally, we shall give some necessary and sufficient conditions so that a plant is strongly stabilizable (i.e. stabilizable by a stable controller) and prove that every internally stabilizable MIMO plant over A = H# (C+ ) is strongly stabilizable.
Internal and External Stability and Robust Stability Condition for a Class of InfiniteDimensional Systems
 Automatica
, 1991
"... In the current study of robust stability of infinitedimensional systems, internal exponential stability is not necessarily guaranteed. This paper introduces a new class of impulse responses called in which the usual notion of L input/output stability guarantees not only external but also inter ..."
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Cited by 2 (2 self)
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In the current study of robust stability of infinitedimensional systems, internal exponential stability is not necessarily guaranteed. This paper introduces a new class of impulse responses called in which the usual notion of L input/output stability guarantees not only external but also internal exponential stability. The result is applied to derive a closedloop stability condition, and a version of the small gain theorem with internal exponential stability; this leads to a robust stability condition that also assures internal stability. An application to repetitive control systems is shown to illustrate the results.
On the existence of approximately coprime factorizations for retarded systems,” Systems and Control Letters 13(1989
"... establishes a result linking algebraically coprime factorizations of transfer matrices of delay systems to approximately coprime factorizations in the sense of distributions. The latter have been employed by the second author in the study of functionspace controllability for such systems. ..."
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Cited by 2 (0 self)
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establishes a result linking algebraically coprime factorizations of transfer matrices of delay systems to approximately coprime factorizations in the sense of distributions. The latter have been employed by the second author in the study of functionspace controllability for such systems.
Coprimeness Conditions For Pseudorational Transfer Functions
"... Coprimeness conditions play important roles in various aspects of system/control theory: realization, controllability, stabilization, just to name a few. While the issue is now well understood for finitedimensional systems, it is far from being settled for infinitedimensional systems. This is due ..."
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Coprimeness conditions play important roles in various aspects of system/control theory: realization, controllability, stabilization, just to name a few. While the issue is now well understood for finitedimensional systems, it is far from being settled for infinitedimensional systems. This is due to a wide variety of situations in which this issue occurs, and several variants of coprimeness notions, which are equivalent in the finitedimensional context, turn out to be nonequivalent. This paper studies the notions of spectral, approximate and exact coprimeness for pseudorational transfer functions. A condition is given under which these notions coincide. 1
Equivalent Characterization of Invariant Subspaces and Applications to Optimal Sensitivity Problem
 Systems Control Lett
"... This paper gives some equivalent characterizations for invariant subspaces of H , when the underlying structure is specified by the socalled pseudorational transfer functions. This plays a fundamental role in computing the optimal sensitivity for a certain important class of infinitedimensional ..."
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This paper gives some equivalent characterizations for invariant subspaces of H , when the underlying structure is specified by the socalled pseudorational transfer functions. This plays a fundamental role in computing the optimal sensitivity for a certain important class of infinitedimensional systems, including delay systems. A closed formula, easier to compute than the wellknown ZhouKhargonekar formula, is given for optimal sensitivity for such systems. An example is given to illustrate the result. 1
Minimal Representations for Delay Systems
"... Abstract: There are many, nonequivalent notions of minimality in state space representations for delay systems. In this class, one can express the transfer function as a ratio of two exponential polynomials. Then one can introduce various notions of coprimeness in such a representation. For example, ..."
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Abstract: There are many, nonequivalent notions of minimality in state space representations for delay systems. In this class, one can express the transfer function as a ratio of two exponential polynomials. Then one can introduce various notions of coprimeness in such a representation. For example, if there is no common zeros between the numerator and denominator, it corresponds to a spectrally minimal realization, i.e., all eigenspaces are reachable. Another fact is that if the numerator and denominator are approximately coprime in some sense, then it corresponds to approximate reachability. All these are nicely embraced in the class of pseudorational transfer functions introduced by the author. The central question here is to characterize the Bézout identity in this class. This is shown to correspond to a noncancellation property in the extended complex plane, including infinity. This leads to a unified understanding of coprimeness conditions for commensurate and noncommensurable delay cases. Various examples are examined in the light of the general theorem obtained here. 1.