This paper considers the problem of robust eigenstructure assignment, which involves finding a feedback gain matrix that makes the closed-loop system insensitive to perturbations or parameter variations. The main contribution of the paper is to derive a new robustness measure using the matrix perturbation theory. The new measure is used to formulate a new method for robust control of the system...

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

In this paper, we improve a result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders. Given a (1−ε)-satisfiable instance of Unique Games with the constraint graph G, our algorithm finds an assignment satisfying at least a 1 − Cε/hG fraction of all constraints if ε < cλG where hG is the edge expansion of G, λG is the second smallest eigenvalue...

The studied linear discrete-continuous system contains two coupled subsystems: one with continuous-time dynamics, the other with discrete-time dynamics. Continuoustime dynamics are described by ordinary linear differential equations, whereas discretetime dynamics are described by difference equations for the system state jumps at prescribed time instants. Systems of three following degrees of g...

The quadratic assignment problem (denoted QAP), in the trace formulation over the permutation matrices, is min X2 tr(AXB + C)X t : Several recent lower bounds for QAP are discussed. These bounds are obtained by applying continuous optimization techniques to approximations of this combinatorial optimization problem, as well as by exploiting the special matrix structure of the problem. In particu...

The partial quadratic eigenvalue assignment problem (PQEAP) is to compute a pair of feedback matrices such that a small number of unwanted eigenvalues in a structure are reassigned to suitable locations while keeping the remaining large number of eigenvalues and the associated eigenvectors unchanged. The problem arises in active vibration control of structures. For real-life applications, it is...

Finding global optimum of a non-convex quadratic function is in general a very difficult task even when the feasible set is a polyhedron. We show that when the feasible set of a quadratic problem consists of orthogonal matrices from Rn×k, then we can transform it into a semidefinite program in matrices of order kn which has the same optimal value. This opens new possibilities to get good lower ...