Sistemas singulares y matrices polinomiales

There is a one-to-one correspondence between the set of quadruples of matrices defining singular linear time-invariant dynamical systems and a subset of the set of polynomial matrices. This correspondence preserves the equivalence relations introduced in both sets (feedback-similarity and strict equivalence): two quadruples of matrices are feedback-equivalent if, and only if, the polynomial matrices associated to them are also strictly equivalent. Los sistemas lineales singulares (DAEs) y su control han sido extensamente estudiados a partir de la d´ecada de 1970 (v´eanse, por ejemplo, [1], [2], [3], [4], [6], [7], [8], [10], [11], [12], [15]). Estos sistemas aparecen de forma natural al proponer modelos para distintos tipos de sistemas: mecánicos, eléctricos, económicos, etc. En esta exposici´on se aborda el problema de estudiar la biyecci´on que existe entre los sistemas lineales singulares invariantes en el tiempo con la relación de equivalencia que denominaremos “equivalencia por realimentación” (y que generaliza la equivalencia por bloques en el caso de parejas de matrices) y la “equivalencia estricta” extendida a matrices polinomiales de orden cualquiera, probándose que esta correspondencia preserva las relaciones de equivalencia introducidas en ambos conjuntos

Realization and partial fractions

AbstractWe discuss the relation between two intrinsically different proposals that have been made in the literature concerning the representation by constant matrices of rational matrices given in fractional form. It turns out that the relation is most naturally studied in the framework of partial-fraction decompositions. We develop the realization theory for decompositions with respect to arbitrary complementary parts of the extended complex plane which may, for instance, correspond to stability and instability. An isomorphism is obtained which connects the spaces used in the two methods, and several identities relating to the McMillan degree are derived in a direct way. Finally, a new computational procedure is given to obtain the partial-fraction decomposition of a rational matrix given in fractional form

Structure evolving systems and control in integrated design

Existing methods in Systems and Control deal predominantly with Fixed Systems, that have been designed in the past, and for which the control design has to be performed. The new paradigm of Structure Evolving Systems (SES), expresses a new form of system complexity where the components, interconnection topology, measurement-actuation schemes may not be fixed, the control scheme also may vary within the system-lifecycle and different views of the system of varying complexity may be required by the designer. Such systems emerge in many application domains and in the engineering context in problems such as integrated system design, integrated operations, re-engineering, lifecycle design issues, networks, etc. The paper focuses on the Integrated Engineering Design (IED), which is revealed as a typical structure evolution process that is strongly linked to Control Theory and Design type problems. It is shown, that the formation of the system, which is finally used for control design evolves during the earlier design stages and that process synthesis and overall instrumentation are critical stages of this evolutionary process that shapes the final system structure and thus the potential for control design. The paper aims at revealing the control theory context of the evolutionary mechanism in overall system design by defining a number of generic clusters of system structure evolution problems and by establishing links with existing areas of control theory. Different aspects of model evolution during the overall design are identified which include cases such as: (i) Time-dependent evolution of system models from “early” to “late” stages of design. (ii) Design stage-dependent evolution from conceptualisation to process synthesis and to overall instrumentation. (iii) Redesign of given systems and constrained system evolution. Within each cluster a number of well defined new Control Theory problems are introduced, which may be studied within the structural methodologies framework of Linear Systems. The problems posed have a general systems character, but the emphasis here is on Linear Systems; an overview of relevant results is given and links with existing research topics are established. The paper defines the Structural Control Theoretic context of an important family of complex systems emerging in engineering design and defines a new research agenda for structural methods of Control Theory