Decomposition Of Linear Systems Research Articles

Decomposition of Linear Systems on Disconnected Lie Groups

Decomposition of Linear Systems on Disconnected Lie Groups

Some Categorical Properties of Linear Systems

Linear control systems are studied by means of a state-space approach. Feedback morphisms are presented as natural generalization of feedback equivalences. The set of feedback morphisms between two linear systems is a vector space. Kernels, cokernels, as well as monomorphisms, epimorphisms, sections, and retracts of feedback morphisms are studied in the category of linear systems over finite dimensional vector spaces. Finally, a classical Kalman’s decomposition of linear systems over vector spaces is presented as a split short exact sequence in the category.

Groups of Congruences and Restriction Matrices

Let Ω be a domain of the Euclidean space R m sent onto itself by a finite group G of congruences. In this paper we first define M elementary restriction matrices related to the group G and to a system of irreducible matrix representations of G. We then describe a general procedure to generate M restriction matrices for any finite-dimensional space V(Ω) of real functions defined on Ω, when V(Ω) is invariant with respect to G. The number M depends only on the group G. Restriction matrices for the space V(Ω) have a block structure and all blocks can be obtained as from an elementary restriction matrix. Restriction matrices related to V(Ω) define a decomposition of V(Ω) as the sum of M subspaces. Finally, owing to restriction matrices, we propose a result of decomposition for linear systems. Several examples are presented.

Angle-only tracking filter in modified spherical coordinates

References Gregory, C. Z., Jr., of Large Flexible Spacecraft Models Using Internal Balancing Theory,'* Journal of Guidance, Control, and Dynamics, Vol. 7, 1984, pp. 725-732. Moore, B. C., Principal Analysis in Linear Systems: Controllability, Observability, and Reduction, IEEE Transactions on Automatic Control, Vol. AC-26, 1981, pp. 17-32. Gawronski, W., and Williams, T., Model Reduction for Flexible Space Proceedings of the AIAA/ASME/ASCE/AHS/ ASC30th Structures, Structural Dynamics and Materials Conference, AIAA, Washington, DC, 1989, pp. 1555-1565. Gawronski, W., and Juang, J.-N., Near-Optimal Reduction in Balanced and Modal Coordinates, Proceedings of 26th Annual A llerton Conference on Communication, Control and Computing, Sept. 1988, pp. 209-219. Skelton, R. E., Decomposition of Linear Systems with Application to Reduction, International Journal of Control, Vol. 32, No. 6, 1980, pp. 1031-1055. Skelton, R. E., and Yousuff, A., Component Cost Analysis of Large Scale Systems, International Journal of Control, Vol. 37, No. 2, 1983, pp. 285-304. Clough, R. W., and Penzien, J., Dynamics of Structures, McGraw-Hill, New York, 1975. Angle-Only Tracking Filter in Modified Spherical Coordinates

A decomposition theory for matroids. V. Testing of matrix total unimodularity

We present an O(( m + n) 3) algorithm for deciding total unimodularity of any real m × n matrix, i.e., for deciding whether or not every square submatrix of the given matrix has determinant 0 or ±1. The algorithm relies on the well-known reduction to the binary case, but from then on is quite different from any method we know of, in particular, from the prior algorithm by W. H. Cunningham and J. Edmonds (Decomposition of linear systems, in preparation) and the recent algorithm by R. E. Bixby, W. H. Cunningham, and A. Rajan (“A Decomposition Algorithm for Matroids,” Working Paper, Rice University 1986), which are of order O(( m + n) 5) and O(( m + n) 4.5 (log( m + n)) 0.5), respectively. The most difficult part of the algorithm, where regularity of a 3-connected, binary, nongraphic, and noncographic matroid must be decided, is handled by a search procedure that relies on the concept of induced decompositions of Parts III and IV. The efficacy of that search procedure crucially depends on asymmetries between certain circuit results and cocircuit results of graphs. In other settings these asymmetries can be quite annoying, but here they turn out to be most beneficial.