The controllability Gramian of lattice graphs

Automatica ◽  
2020 ◽  
Vol 114 ◽  
pp. 108833 ◽  
Author(s):  
Isaac Klickstein ◽  
Francesco Sorrentino
Keyword(s):  
Controllability Gramian ◽  
Lattice Graphs

A problem on lattice graphs. Theory and algorithm

Cybernetics ◽  
1981 ◽  
Vol 16 (4) ◽  
pp. 628-631
Author(s):  
L. A. Klygina
Keyword(s):  
Lattice Graphs

scholarly journals Convergence Theorems for Some Layout Measures on Random Lattice and Random Geometric Graphs

2000 ◽  
Vol 9 (6) ◽  
pp. 489-511 ◽  
Author(s):  
JOSEP DÍAZ ◽  
MATHEW D. PENROSE ◽  
JORDI PETIT ◽  
MARÍA SERNA
Keyword(s):  
Constant Factor ◽  
Geometric Graphs ◽  
Convergence Theorems ◽  
Linear Arrangement ◽  
Random Lattice ◽  
Random Geometric Graphs ◽  
Unit Square ◽  
Subcritical Regime ◽  
Probabilistic Setting ◽  
Lattice Graphs

This work deals with convergence theorems and bounds on the cost of several layout measures for lattice graphs, random lattice graphs and sparse random geometric graphs. Specifically, we consider the following problems: Minimum Linear Arrangement, Cutwidth, Sum Cut, Vertex Separation, Edge Bisection and Vertex Bisection. For full square lattices, we give optimal layouts for the problems still open. For arbitrary lattice graphs, we present best possible bounds disregarding a constant factor. We apply percolation theory to the study of lattice graphs in a probabilistic setting. In particular, we deal with the subcritical regime that this class of graphs exhibits and characterize the behaviour of several layout measures in this space of probability. We extend the results on random lattice graphs to random geometric graphs, which are graphs whose nodes are spread at random in the unit square and whose edges connect pairs of points which are within a given distance. We also characterize the behaviour of several layout measures on random geometric graphs in their subcritical regime. Our main results are convergence theorems that can be viewed as an analogue of the Beardwood, Halton and Hammersley theorem for the Euclidean TSP on random points in the unit square.

Characterization of triangular and lattice graphs

1998 ◽  
Vol 39 (5) ◽  
pp. 908-912 ◽  
Author(s):  
V. V. Kabanov
Keyword(s):  
Lattice Graphs

Enumeration of perfect matchings of lattice graphs by Pfaffians

2018 ◽  
Vol 338 ◽  
pp. 412-420
Author(s):  
Xing Feng ◽  
Lianzhu Zhang ◽  
Mingzu Zhang
Keyword(s):  
Perfect Matchings ◽  
Lattice Graphs

Layout Problems on Lattice Graphs

1999 ◽  
pp. 103-112 ◽  
Author(s):  
Josep Díaz ◽  
Mathew D. Penrose ◽  
Jordi Petit ◽  
María Serna
Keyword(s):  
Lattice Graphs

An Efficient Approximated Algorithm for Balancing and Order Reduction of Lightly Damped Systems

1995 ◽  
Author(s):  
Yoram Halevi
Keyword(s):  
Substantial Reduction ◽  
Mechanical Systems ◽  
Order Reduction ◽  
Transformation Matrix ◽  
Special Structure ◽  
Reduced Order ◽  
Controllability Gramian ◽  
Balancing Transformation ◽  
Damped Systems ◽  
Observability Gramian

Abstract A method of approximating the controllability gramian, observability gramian and the balancing transformation for lightly damped mechanical systems is presented, the approximation uses the special structure of the system and the fact that the damping is small to reduce the amount of computation considerably. Furthermore, one can avoid the calculation of the entire balancing transformation matrix and calculate only the parts that are required for order reduction. In cases where the reduced order is much smaller than the original that leads to another substantial reduction of computation effort.

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