In this paper, a possible solution of the basic nonlinear quadratic matrix equation was proposed. The solution is crucial in the formulation of the particular criteria for the delay-dependent finite time stability of discrete time delay systems represented as x(k+1) = A0(k) + A1x(k–h). The time delay-dependent criteria have been derived. In addition, the significance of the nonlinear discrete p...

This paper examines the relationship between the dynamics of large networks and of their smaller factor-networks (factors) obtained through the factorization of the network's graph representation. We speci cally examine dynamics of networks which have Z-matrix state matrices. We perform a Cartesian product decomposition on its network structure producing factors which also have Z-matrix dynamic...

We consider multi-grid, or more appropriately, multi-level techniques for the numerical solution of operator Lyapunov and algebraic Riccati equations. The Riccati equation, which is quadratic, plays an essential role in the solution of linear-quadratic optimal control problems. The linear Lyapunov equation is important in the stability theory for linear systems and its solution is the primary s...

We consider multi-grid, or more appropriately, multi-level techniques for the numerical solution of operator Lyapunov and algebraic Riccati equations. The Riccati equation, which is quadratic, plays an essential role in the solution of linear-quadratic optimal control problems. The linear Lyapunov equation is important in the stability theory for linear systems and its solution is the primary s...

We study the solvability of a nonlinear quadratic integral equation of Hammerstein type. Using the technique of measures of noncompactness we prove that this equation has solutions on an unbounded interval. Moreover, we also obtain an asymptotic characterization of these solutions. Several special cases of this integral equation are discussed and applications to real world problems are indicate...

We prove an existence theorem for a quadratic functional-integral equation of mixed type. The functional-integral equation studied below contains as special cases numerous integral equations encountered in nonlinear analysis. With help of a suitable measure of noncompactness, we show that the functional integral equation of mixed type has solutions being continuous and bounded on the interval [...