Internal positivity offers a computationally cheap certificate for external (input-output) of linear time-invariant system. However, the drawback with this lies in its realization dependency. First, computing such requires finding polyhedral cone potentially high number extremal generators that lifts dimension state-space representation, significantly. Second, not all externally positive system...

A new family of minimal spectrally arbitrary patterns is presented which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [J.H. Drew, C.R. Johnson, D.D. Olesky, and P. van den Driessche. Spectrally arbitrary patterns.Lin. Alg. and Appl. 308:121137, 2000]. The novel approach here is the use of the Intermediate Value Theorem to avoid finding an explicit nilpotent ...

A new family of minimal spectrally arbitrary patterns is presented which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [J.H. Drew, C.R. Johnson, D.D. Olesky, and P. van den Driessche. Spectrally arbitrary patterns.Lin. Alg. and Appl. 308:121137, 2000]. The novel approach here is the use of the Intermediate Value Theorem to avoid finding an explicit nilpotent ...

It has been shown [2] that adiabatic switching can significantly reduce the dynamic power dissipation in an integrated circuit. Due to the overhead in the realization of adiabatic logic blocks [3] the best results are achieved when it is used only for charging dominant loads in an integrated circuit [7]. It has been demonstrated [4] that a multi stage driver is needed for minimal power dissipat...

It has been shown (Athas et al., 1994) that adiabatic switching can significantly reduce the dynamic power dissipation in an integrated circuit. Due to the overhead in the realization of adiabatic logic blocks (Saas et al., 2000) the best results are achieved when it is used only for charging dominant loads in an integrated circuit (Voss and Glessner, 2001). It has been demonstrated (Saas et al...

In this paper, the one-dimensional Gray–Markel lattice-ladder discrete filter structure is extended to two dimensions (2D). The proposed 2D circuit implementation has minimal number of unit delays. Based on this circuit implementation the corresponding 2D state space realization is derived. The matrices A, b, c and the scalar d of the 2D state space model are presented in generalized closed for...

We propose computationally efficient and numerically reliable algorithms to compute minimal realizations of periodic descriptor systems. The main computational tool employed for the structural analysis of periodic descriptor systems (i.e., reachability and observability) is the orthogonal reduction of periodic matrix pairs to Kronecker-like forms. Specializations of a general reduction algorith...

We investigate which rst-order representations can be obtained from high-order representations of linear systems`by inspection', that is just by rearrangement of the data. Under quite weak conditions it is possible to obtain minimal realizations in the so-called pencil form; under stronger conditions one can obtain minimal realizations in standard state space form by inspection. The development...

Describing configuration spaces of 1-degree-of-freedom (1-dof) linkages in 2D is a difficult problem with a long history. We use the Cayley configuration space, a set of intervals of possible distance-values for an independent non-edge. We study the following complexity measures (associated with the linkage’s underlying graph): (a) Cayley size, i.e., the number of intervals, (b) Cayley computat...

This paper addresses three questions related to minimal triangulations of a three-dimensional convex polytope P. • Can the minimal number of tetrahedra in a triangulation be decreased if one allows the use of interior points of P as vertices? • Can a dissection of P use fewer tetrahedra than a triangulation? • Does the size of a minimal triangulation depend on the geometric realization of P? Th...