A new solution approach to polynomial LPV system analysis and synthesis

Based on sum-of-squares (SOS) decomposition, we propose a new solution approach for polynomial LPV system analysis and control synthesis problems. Instead of solving matrix variables over a positive definite cone, the SOS approach tries to find a suitable decomposition to verify the positiveness of given polynomials. The complexity of the SOS-based numerical method is polynomial of the problem size. This approach also leads to more accurate solutions to LPV systems than most existing relaxation methods. Several examples have been used to demonstrate benefits of the SOS-based solution approach

Groups in Which Commutativity Is a Transitive Relation

AbstractWe investigate the structure of groups in which commutativity is a transitive relation on non-identity elements (CT-groups). A detailed study of locally finite, polycyclic, and torsion-free solvableCT-groups is carried out. Other topics include fixed-point-free groups of automorphisms of abelian torsion groups and their cohomology groups

Stabilizer Approximation III: Maximum Cut

We apply the stabilizer formalism to the Maximum Cut problem, and obtain a new greedy construction heuristic. It turns out to be an elegant synthesis of the edge-contraction and differencing edge-contraction approaches. Utilizing the relation between the Maximum Cut problem and the Ising model, the approximation ratio of the heuristic is easily found to be at least $1/2$. Moreover, numerical results show that the heuristic has very nice performance for graphs with about 100 vertices.Comment: Proves that the approximation ratio is at least 1/2; greatly improves the implementation of the algorithm. 14 pages, 2 figure