Analytic system problems and J-lossless coprime factorization for infinite-dimensional linear systems

AbstractThis paper extends the coprime factorization approach to the synthesis of internally stabilizing controllers satisfying an H∞-norm bound to a class of systems with irrational transfer matrices. Using the coprime factorization description, the H∞-control problem can be reduced to two stable analytic system problems. Such problems have solutions if and only if a certain J-lossless factorization exists. The full H∞-synthesis problem is shown to be equivalent to the solution of two nested J-lossless factorizations. If the irrational transfer matrix has a state-space realization, then the known state-space formulas for the H∞-control problem may be recovered using the relationship between J-lossless factorizations and solutions of Riccati equations. However, the results derived here are valid for a larger class of infinite-dimensional systems

Finite-time behavior of inner systems

In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller

BIBO stability robustness in the presence of coprime factor perturbations

Cover title.Includes bibliographical references (leaf 8).Research supported by the Center for Intelligent Control Systems under an Army Research Office grant. DAAL03-86-K-0171 Research supported by the NSF. 8810178-ECSM.A. Dahleh

Modeling and control of TCV

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