The aim of this paper is to analyze the undamped second order descriptor systems to show the possibility of transform an undamped second order descriptor system to a pure first order descriptor system ,on different ways, while stating some of its benefits. Meanwhile we will introduce pure first order systems and undamped second order systems and indicate that under some assumptions every undamp...

the aim of this paper is to analyze the undamped second order descriptor systems to show the possibility of transform an undamped second order descriptor system to a pure first order descriptor system ,on different ways, while stating some of its benefits. meanwhile we will introduce pure first order systems and undamped second order systems and indicate that under some assumptions every undamp...

In this paper the stabilization problem of undamped second order system is considered. The stabilization by first order dynamic feedback is studied. The global asymptotic stability of the respectively closed-loop system is proved by LaSalle’s theorem. As an example of application of the proposed method an electric ladder network L and lc type is presented. Numerical calculations were made using...

In this paper, structure preserving order reduction of proportionally damped and undamped second order systems is presented. The discussion is based on Second Order Krylov Subspace method and it is shown that for systems with a proportional damping, the damping matrix does not contribute to the projection matrices and the reduction can be carried out using the classical Krylov subspaces. As a r...

where g and p are real valued functions continuous on the reals R , p(t+2n) = p(t), and the solutions of (1) are uniquely determined by their initial conditions. If g is nonlinear, the question of whether all solutions of (1) are bounded on R has long been recognized as nontrivial and challenging. For the special case of g(x) = 2x Morris [1] was able to show that this question has an affirmativ...

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual off-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in th...

It is shown how to obtain asymptotic stability in second-order undamped systems using time-delay action in the feedback of position. The effect of the delay is similar to derivative feedback in modifying the behavior of the system. Results are given on the selection of the controller parameters both in the absence and the presence of additional delay in the feedback path. The time-lag position ...