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001 Some remarks on a new characterization of linear controllability
Abstracts Abstracts in this section are from papers presented at: I F A C W O R K S H O P ON SYSTEM STRUCTURE AND CONTROL Prague. Czech Republic. 3-5 September 1992 Full papers appear in the Pergamon Press publication of the above meeting, to which the page numbers relate. (ISBN: O 08 042057 5)
*Full paper published in this issue
001 Some Remarks on a New Characterization of Linear Controllability M. Flless, pp 8-11
005 Fixed D e g r ~ Solutions of Polynomial Equations V. Kuceru, pp 24-26 Given the linear polynomial equation AX + BY = C, this paper considers the existence of solution pairs X,Y having prespeeifled degrees, and parameterizes all such pairs. This result proves useful in the analysis and design of linear control systems.
A module-theoretic approach to linear controllability is shown to be equivalent to Willems' trajectory characterization. The paper also sketches a computationfree derivation of Brunovsky's canonical form and shows how to relate the notion of numerical state-space to the algebraic standpoint taken.
006 Free End-Point Linear-Quadratk Control Subject to Implicit Continuous-Time Systems: Necessary and Sufficient Conditions for Solvability T. Geerts, pp 28-31
002 The Direct (Inverse) Nyquist Array and Quantitative Feedback Theory Approaches to Multivariable Feedback Design: A Structural Assessment for 2-Input 2-Output Systems J. O'Reilly, W.E. Lelthead, pp 12-15
For an implicit continuous-time system with arbitrary constant coefficients, necessary and sufficient conditions are derived for solvability of the associated free endpoint linear-quadratic optimal control problem. This problem turns out to be solvable if and only if the underlying system is output stabilized, as is the case for a standard system.
A new applications-oriented approach - Individual Channel Design - to multivariable feedback control was shown in earlier papers to be a transparent, flexible and supportive design methodology which directly aims to meet the user's control requirements and is well-suited to the engineering context. This paper addresses the relationship of Individual Channel Design to earlier frequency-domain methods for multivariable design. It also provides an interpretation and assessment of two important frequency-domain methods, highlights their advantages and establishes for what classes of multivariable problems they are valid. The investigation focuses on 2-input 2-output multivariable systems; the conclusions extend, with the necessary changes, to general m-input m-output systems.
007 Strictly Doubly CoprimeFuctorizations Related to Reduced Order Observers
P. Hippe, pp 32-35 The factorization approach uses fractional representations for the system and the compensator transfer matrices - the so called "doubly coprime factorizations" (DCFs). These DCFs may contain identity elements in the ring of stable proper transfer matrices, i.e. pole zero cancellations within the left half s-plane. The introduction of such cancelling factors seems necessary when defining DCFs related to reduced order observers. It is shown that such DCFs not containing identity elements can be defined. To distinguish them from the usual DCFs the notion of strictly double coprime factorization (SDCFs) is introduced. It is shown how these SDCFs can be used in the design of all stabilizing compensators.
003 Feedback Realization of Open Loop Diagonalizers
V. Eldem, pp 16-22 In this work the feedback realization of open loop diagonalizers (old) of a linear, time-variant multivariable system is considered. In the first part of the paper, the properties of o/ds which admit i) dynamic state feedback, ii) constant state feedback, iii) dynamic output feedback and iv) constant output feedback are investigated. Then, in the second part, dynamic (constant) output feedback deeoupling problems are formulated as determining an open loop diagonalizer which admits the desired feedback realization.
008 Generalized Bezoutlan for Discrete-Time Linear Periodic Systems C. Coil, R. Bru, V. Hern6ndez, pp 36-39
004 Polynomial Formulation of Morgan's Problem
This paper introduces the concept of periodic generalized Bezoutians associated to discrete-tune linear periodic systems or periodic rational matrices. Given a collection of periodic rational matrices, the dimension of minimal realizations is characterized by means of the rank of the periodic generalized Bezoutian matrix.
P. Zagalak, J.F. Lafay, J J . Lolseau, pp 20-22 Morgan's Problem is reconsidered, and new and explicit necessary conditions are established for there to exist a solution to this problem.
385
*Full paper published in this issue
001 Some Remarks on a New Characterization of Linear Controllability M. Flless, pp 8-11
005 Fixed D e g r ~ Solutions of Polynomial Equations V. Kuceru, pp 24-26 Given the linear polynomial equation AX + BY = C, this paper considers the existence of solution pairs X,Y having prespeeifled degrees, and parameterizes all such pairs. This result proves useful in the analysis and design of linear control systems.
A module-theoretic approach to linear controllability is shown to be equivalent to Willems' trajectory characterization. The paper also sketches a computationfree derivation of Brunovsky's canonical form and shows how to relate the notion of numerical state-space to the algebraic standpoint taken.
006 Free End-Point Linear-Quadratk Control Subject to Implicit Continuous-Time Systems: Necessary and Sufficient Conditions for Solvability T. Geerts, pp 28-31
002 The Direct (Inverse) Nyquist Array and Quantitative Feedback Theory Approaches to Multivariable Feedback Design: A Structural Assessment for 2-Input 2-Output Systems J. O'Reilly, W.E. Lelthead, pp 12-15
For an implicit continuous-time system with arbitrary constant coefficients, necessary and sufficient conditions are derived for solvability of the associated free endpoint linear-quadratic optimal control problem. This problem turns out to be solvable if and only if the underlying system is output stabilized, as is the case for a standard system.
A new applications-oriented approach - Individual Channel Design - to multivariable feedback control was shown in earlier papers to be a transparent, flexible and supportive design methodology which directly aims to meet the user's control requirements and is well-suited to the engineering context. This paper addresses the relationship of Individual Channel Design to earlier frequency-domain methods for multivariable design. It also provides an interpretation and assessment of two important frequency-domain methods, highlights their advantages and establishes for what classes of multivariable problems they are valid. The investigation focuses on 2-input 2-output multivariable systems; the conclusions extend, with the necessary changes, to general m-input m-output systems.
007 Strictly Doubly CoprimeFuctorizations Related to Reduced Order Observers
P. Hippe, pp 32-35 The factorization approach uses fractional representations for the system and the compensator transfer matrices - the so called "doubly coprime factorizations" (DCFs). These DCFs may contain identity elements in the ring of stable proper transfer matrices, i.e. pole zero cancellations within the left half s-plane. The introduction of such cancelling factors seems necessary when defining DCFs related to reduced order observers. It is shown that such DCFs not containing identity elements can be defined. To distinguish them from the usual DCFs the notion of strictly double coprime factorization (SDCFs) is introduced. It is shown how these SDCFs can be used in the design of all stabilizing compensators.
003 Feedback Realization of Open Loop Diagonalizers
V. Eldem, pp 16-22 In this work the feedback realization of open loop diagonalizers (old) of a linear, time-variant multivariable system is considered. In the first part of the paper, the properties of o/ds which admit i) dynamic state feedback, ii) constant state feedback, iii) dynamic output feedback and iv) constant output feedback are investigated. Then, in the second part, dynamic (constant) output feedback deeoupling problems are formulated as determining an open loop diagonalizer which admits the desired feedback realization.
008 Generalized Bezoutlan for Discrete-Time Linear Periodic Systems C. Coil, R. Bru, V. Hern6ndez, pp 36-39
004 Polynomial Formulation of Morgan's Problem
This paper introduces the concept of periodic generalized Bezoutians associated to discrete-tune linear periodic systems or periodic rational matrices. Given a collection of periodic rational matrices, the dimension of minimal realizations is characterized by means of the rank of the periodic generalized Bezoutian matrix.
P. Zagalak, J.F. Lafay, J J . Lolseau, pp 20-22 Morgan's Problem is reconsidered, and new and explicit necessary conditions are established for there to exist a solution to this problem.
385