1,199 research outputs found
On Pole Placement and Invariant Subspaces
The classical eigenvalue assignment problem is revisited in this note. We
derive an analytic expression for pole placement which represents a slight
generalization of the celebrated Bass-Gura and Ackermann formulae, and also is
closely related to the modal procedure of Simon and Mitter.Comment: Presented at ICAT201
Continuity argument revisited: geometry of root clustering via symmetric products
We study the spaces of polynomials stratified into the sets of polynomial
with fixed number of roots inside certain semialgebraic region , on its
border, and at the complement to its closure. Presented approach is a
generalisation, unification and development of several classical approaches to
stability problems in control theory: root clustering (-stability) developed
by R.E. Kalman, B.R. Barmish, S. Gutman et al., -decomposition(Yu.I.
Neimark, B.T. Polyak, E.N. Gryazina) and universal parameter space method(A.
Fam, J. Meditch, J.Ackermann).
Our approach is based on the interpretation of correspondence between roots
and coefficients of a polynomial as a symmetric product morphism.
We describe the topology of strata up to homotopy equivalence and, for many
important cases, up to homeomorphism. Adjacencies between strata are also
described. Moreover, we provide an explanation for the special position of
classical stability problems: Hurwitz stability, Schur stability,
hyperbolicity.Comment: 45 pages, 4 figure
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Robust H2/H∞-state estimation for discrete-time systems with error variance constraints
Copyright [1997] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper studies the problem of an H∞-norm and variance-constrained state estimator design for uncertain linear discrete-time systems. The system under consideration is subjected to
time-invariant norm-bounded parameter uncertainties in both the state and measurement matrices. The problem addressed is the design of
a gain-scheduled linear state estimator such that, for all admissible measurable uncertainties, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞-norm upper bound constraint, simultaneously. The conditions for the existence of desired estimators are obtained in terms of matrix inequalities, and the explicit expression of these estimators is also derived. A numerical example is provided to demonstrate various aspects of theoretical results
Asymptotic orders of reachability in perturbed linear systems
Bibliography: p. 36-37.Supported in part by the Army Research Office. DAAG-29-84-K-0005 Supported in part by the Air Force Office of Scientific Research. AFOSR-82-0258Chuneyt M. Özveren, Alan S. Willsky, George C. Verghese
Algebraic geometric methods for the stabilizability and reliability of multivariable and of multimode systems
The extent to which feedback can alter the dynamic characteristics (e.g., instability, oscillations) of a control system, possibly operating in one or more modes (e.g., failure versus nonfailure of one or more components) is examined
Robust eigenstructure assignment in geometric control theory
In this paper we employ the Rosenbrock system matrix pencil for the computation of output-nulling subspaces of linear time-invariant systems which appear in the solution of a large number of control and estimation problems. We also consider the problem of finding friends of these output-nulling subspaces, i.e., the feedback matrices that render such subspaces invariant with respect to the closed-loop map and output-nulling with respect to the output map, and which at the same time deliver a robust closed-loop eigenstructure. We show that the methods presented in this paper offer considerably more robust eigenstructure assignment than the other commonly used methods and algorithms
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