A complete classification is presented of elliptic and K3 fibrations birational to certain mildly singular complex Fano 3-folds. Detailed proofs are given for one example case, namely that of a general hypersurface X of degree 30 in weighted P with weights 1,4,5,6,15; but our methods apply more generally. For constructing birational maps from X to elliptic and K3 fibrations we use Kawamata blow...

In this article, we study the initial value problem of a non-homogeneous singular linear discrete time system whose coefficients are either non-square constant matrices or square with an identically zero matrix pencil. By taking into consideration that the relevant pencil is singular, we provide necessary and sufficient conditions for existence and uniqueness of solutions. More analytically we ...

In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary (but finite) number of dropping sections and approximating some continuous nonlinear function. Studying all possible local and global bifurcations of its limit cycles, we prove that such a piecewise linear dynamical system with k dropping sections and 2k + 1 singular points can have at ...

In linear system theory, the Hankel singular values are often computed in a state space setting using the product of Gramian matrices. They are known, however, to be intrinsically dependent only on the input-output map and not on any choice of state space coordinates. In the nonlinear case, there are well defined notions of singular value functions and a Hankel operator, but the connections bet...

 Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...

in this paper robust pid control of fully-constrained cable driven parallel manipulators with elastic cables is studied in detail. in dynamic analysis, it is assumed that the dominant dynamics of cable can be approximated by linear axial spring. to develop the idea of control for cable robots with elastic cables, a robust pid control for cable driven robots with ideal rigid cables is firstly de...

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An infinite horizon H state-feedback control problem for singularly perturbed linear systems with a small state delay is considered. An asymptotic solution of the hybrid system of Riccati-type algebraic, ordinary differential, and partial differential equations with deviating arguments, associated with this problem, is constructed. Based on this asymptotic solution, conditions for the existenc...

This paper deals with a design method of compensation law for linear constrained systems. By employing singular value decomposition of linear systems, we provide a design method of compensation law which fulfills system constraints. The feature of resulting compensation law is illustrated with numerical examples. Copyright c ©2005 IFAC

An H∞ control problem for linear systems with point-wise and distributed state delays is considered. The case, where the output equation does not contain the control variable, is treated. In this case, the problem is singular, i.e., the gametheoretic Riccati equation approach is not applicable to its solution. A method of solution of this problem, based on its regularization and asymptotic solu...