‎In this paper we consider the minimization of a positive semidefinite quadratic form‎, ‎having a singular corresponding matrix $H$‎. ‎We state the dual formulation of the original problem and treat both problems only using the vectors $x in mathcal{N}(H)^perp$ instead of the classical approach of convex optimization techniques such as the null space method‎. ‎Given this approach and based on t...

In this paper some new results concerning linear quadratic regulator (LQR) design for lossless systems are proved. The first result gives a necessary and sufficient condition which allows to obtain directly the optimal gains of an LQR problem for a lossless system, without solving the CARE equation, when a particular quadratic index is considered. The given results can also be viewed as an inve...

The linear quadratic (LQ) optimal control problem is studied for a partial differential equation model of a time-varying plug flow tubular reactor. First some properties of the linearized model around a specific equilibrium profile are studied. Next, an LQ-control feedback is computed by using the corresponding operator Riccati differential equation, whose solution can be obtained via a related...

We study a smoothing Newton method for solving a nonsmooth matrix equation that includes semidefinite programming and the semidefinte complementarity problem as special cases. This method, if specialized for solving semidefinite programs, needs to solve only one linear system per iteration and achieves quadratic convergence under strict complementarity. We also establish quadratic convergence o...

in this paper we consider the solutions of linear systems of saddle point problems‎. ‎by using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the hermitian and skew hermitian splitting method‎.

Lyapunov quadratic functionals are used to test the stability of systems, to compute the critical delay values for time delay systems, to compute the exponential estimates for the solutions of time delay systems, to calculate the robustness bounds for uncertain time delay systems, and to calculate a quadratic performance index for the process of parametric optimization for time delay systems. W...

water quality prediction is a valuable tool for pollutant control in aquatic environments. a river system is selected and one-dimensional flow is assumed for the simulation of pollutant transport in this paper. advective and diffusive terms of transport equation are considered separately. different functions of advective transport are proposed and applied for a specified velocity on the discret...

let $rin textbf{c}^{mtimes m}$ and $sin textbf{c}^{ntimes n}$ be nontrivial involution matrices; i.e., $r=r^{-1}neq pm~i$ and $s=s^{-1}neq pm~i$. an $mtimes n$ complex matrix $a$ is said to be an $(r, s)$-symmetric ($(r, s)$-skew symmetric) matrix if $ras =a$ ($ ras =-a$). the $(r, s)$-symmetric and $(r, s)$-skew symmetric matrices have a number of special properties and widely used in engi...