Results 1  10
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14
A DESCRIPTOR SYSTEMS Toolbox for MATLAB
 Proc. of CACSD’2000 Symposium
"... Abstract: The recently developed PERIODIC SYSTEMS Toolbox for MATLAB is described. The basic approach to develop this toolbox was to exploit the powerful object manipulation features of MATLAB via exible and functionally rich high level mfunctions, while simultaneously enforcing highly efcient an ..."
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Cited by 27 (14 self)
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Abstract: The recently developed PERIODIC SYSTEMS Toolbox for MATLAB is described. The basic approach to develop this toolbox was to exploit the powerful object manipulation features of MATLAB via exible and functionally rich high level mfunctions, while simultaneously enforcing highly efcient and numerically sound computations via the mexfunction technology of MATLAB to solve critical numerical problems. The mfunctions based user interfaces ensure userfriendliness in operating with the functions of this toolbox via an object oriented approach to handle periodic system descriptions. The mexfunctions are based on FORTRAN implementations of recently developed structure exploiting and structure preserving numerical algorithms for periodic systems which completely avoid forming of lifted representations. Copyright c
2005 IFAC
Computing Periodic Deflating Subspaces Associated with a Specified Set of Eigenvalues
 BIT Numerical Mathematics
, 2006
"... We present a direct method for reordering eigenvalues in the generalized periodic real Schur form of a regular Kcylic matrix pair sequence (Ak, Ek). Following and generalizing existing approaches, reordering consists of consecutively computing the solution to an associated Sylvesterlike equation a ..."
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Cited by 12 (5 self)
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We present a direct method for reordering eigenvalues in the generalized periodic real Schur form of a regular Kcylic matrix pair sequence (Ak, Ek). Following and generalizing existing approaches, reordering consists of consecutively computing the solution to an associated Sylvesterlike equation and constructing K pairs of orthogonal matrices. These pairs define an orthogonal Kcyclic equivalence transformation that swaps adjacent diagonal blocks in the Schur form. An error analysis of this swapping procedure is presented, which extends existing results for reordering eigenvalues in the generalized real Schur form of a regular pair (A,E). Our direct reordering method is used to compute periodic deflating subspace pairs corresponding to a specified set of eigenvalues. This computational task arises in various applications related to discretetime periodic descriptor systems. Computational experiments confirm the stability and reliability of the presented eigenvalue reordering method.
On solving discretetime periodic Riccati equations
 In Proc. of 16th IFAC World Congress
, 2005
"... Abstract: Two numerically reliable algorithms to compute the periodic nonnegative definite stabilizing solution of discretetime periodic Riccati equations are proposed. The first method represents an extension of the periodic QZ algorithm to nonsquare periodic pairs, while the second method repres ..."
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Cited by 8 (2 self)
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Abstract: Two numerically reliable algorithms to compute the periodic nonnegative definite stabilizing solution of discretetime periodic Riccati equations are proposed. The first method represents an extension of the periodic QZ algorithm to nonsquare periodic pairs, while the second method represents an extension of a quotientproduct swapping and collapsing ”fast ” algorithm. Both approaches are completely general being applicable to periodic Riccati equations with time varying dimensions as well as with singular control weighting. For the ”fast ” method, reliable software implementation is available in a recently developed PERIODIC SYSTEMS Toolbox. Copyright c ○ 2005 IFAC
Computation of generalized inverses of periodic systems
"... We address the numerically reliable computation of generalized inverses of periodic systems. The underlying inverses are defined via the corresponding lifted representations. Structure preserving reduction of the associated system pencil to a special Kroneckerlike form is the main computational ing ..."
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Cited by 7 (6 self)
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We address the numerically reliable computation of generalized inverses of periodic systems. The underlying inverses are defined via the corresponding lifted representations. Structure preserving reduction of the associated system pencil to a special Kroneckerlike form is the main computational ingredient for the proposed approach. This form can be computed by employing exclusively orthogonal transformations. For the computational algorithm of the generalized inverse, the backward numerical stability can be proved.
An overview of recent developments in computational methods for periodic systems
 In Proceedings of the IFAC Workshop on Periodic Control
, 2007
"... a state of the art survey of computational methods for periodic systems has been presented (Varga and Van Dooren, 2001). This contribution continues this survey by presenting the main achievements in this eld since 2001. Besides many foreseen developments mentioned in 2001 as open problems, importan ..."
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Cited by 6 (0 self)
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a state of the art survey of computational methods for periodic systems has been presented (Varga and Van Dooren, 2001). This contribution continues this survey by presenting the main achievements in this eld since 2001. Besides many foreseen developments mentioned in 2001 as open problems, important new developments took place as general algorithms for analysis of periodic descriptor systems, solution of periodic Riccati equations, or computational methods for continuoustime periodic systems.
Model Reduction of Periodic Descriptor Systems Using Balanced Truncation
"... Abstract Linear periodic descriptor systems represent a broad class of time evolutionary processes in microelectronics and circuit simulation. In this paper, we consider discretetime linear periodic descriptor systems and study the concepts of periodic reachability and observability Gramians. We a ..."
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Cited by 4 (4 self)
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Abstract Linear periodic descriptor systems represent a broad class of time evolutionary processes in microelectronics and circuit simulation. In this paper, we consider discretetime linear periodic descriptor systems and study the concepts of periodic reachability and observability Gramians. We also discuss a lifted representation of periodic descriptor systems and propose a balanced truncation model reduction method for such systems. The behaviour of the suggested model reduction technique is illustrated using a numerical example. 1
Design of fault detection filters for periodic systems
"... We propose a numerically reliable computational approach to design fault detection filters for periodic systems. This approach is based on a new numerically stable algorithm to compute least order annihilators without explicitly building timeinvariant lifted system representations. The main compu ..."
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Cited by 2 (2 self)
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We propose a numerically reliable computational approach to design fault detection filters for periodic systems. This approach is based on a new numerically stable algorithm to compute least order annihilators without explicitly building timeinvariant lifted system representations. The main computation in this algorithm is the orthogonal reduction of a periodic matrix pair to a periodic Kroneckerlike form, from which the periodic realization of the detector is directly obtained.
COMPUTING CODIMENSIONS AND GENERIC CANONICAL FORMS FOR GENERALIZED MATRIX PRODUCTS
 ELECTRONIC JOURNAL OF LINEAR ALGEBRA
, 2011
"... A generalized matrix product can be formally written as A sp p A sp−1 p−1 · · · As2 2 As1 1, where si ∈ {−1, +1} and (A1,..., Ap) is a tuple of (possibly rectangular) matrices of suitable dimensions. The periodic eigenvalue problem related to such a product represents a nontrivial extension of g ..."
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Cited by 2 (2 self)
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A generalized matrix product can be formally written as A sp p A sp−1 p−1 · · · As2 2 As1 1, where si ∈ {−1, +1} and (A1,..., Ap) is a tuple of (possibly rectangular) matrices of suitable dimensions. The periodic eigenvalue problem related to such a product represents a nontrivial extension of generalized eigenvalue and singular value problems. While the classification of generalized matrix products under eigenvaluepreserving similarity transformations and the corresponding canonical forms have been known since the 1970’s, finding generic canonical forms has remained an open problem. In this paper, we aim at such generic forms by computing the codimension of the orbit generated by all similarity transformations of a given generalized matrix product. This can be reduced to computing the so called cointeractions between two different blocks in the canonical form. A number of techniques are applied to keep the number of possibilities for different types of cointeractions limited. Nevertheless, the matter remains highly technical; we therefore also provide a computer program for finding the codimension of a canonical form, based on the formulas developed in this paper. A few examples illustrate how our results can be used to determine the generic canonical form of least codimension. Moreover, we describe an algorithm and provide software for extracting the generically regular part of a generalized matrix product.
On computing minimal realizations of periodic descriptor systems
 Proc. of IFAC Workshop on Periodic Control Systems
"... Abstract: We propose computationally ecient and numerically reliable algorithms to compute minimal realizations of periodic descriptor systems. The main computational tool employed for the structural analysis of periodic descriptor systems (i.e., reachability and observability) is the orthogonal re ..."
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Cited by 2 (1 self)
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Abstract: We propose computationally ecient and numerically reliable algorithms to compute minimal realizations of periodic descriptor systems. The main computational tool employed for the structural analysis of periodic descriptor systems (i.e., reachability and observability) is the orthogonal reduction of periodic matrix pairs to Kroneckerlike forms. Specializations of a general reduction algorithm are employed for particular type of systems. One of the proposed minimal realization methods relies exclusively on structure preserving manipulations via orthogonal transformations for which the backward numerical stability can be proved.