Solid holed torus knot oscillators

In this paper we develop oscillators whose outputs are solid holed torus knots in real three-dimensional space. Here solid holed knots are closed trajectories on the solid holed torus where the solid holed torus is formed by three perpendicular circles revolved around one another. An electronic circuit is presented that can generate any desired solid holed torus knot.Research supported by NSF Grant MIP 87-19886.     

A geometric theory for derivative feedback

The authors use a singular system setting to provide a geometric theory for dynamical systems under derivative feedback. They define the relevant subspace and provide computational design techniques in terms of a generalized Sylvester or Lyapunov equation for which efficient solution techniques are well-known. The authors provide both geometric and algebraic characterizations of the effects of derivative feedback, drawing connections with previous work in state-variable systems as well as extending that work to singular systems     

Output feedback eigenstructure assignment using two Sylvesterequations

The eigenstructure assignment problem with output feedback is studied for systems satisfying the condition p+m> n. The main tool used is the concept of (C, A, B)-invariance and two coupled Sylvester equations, the solution of which leads to the computation of an output stabilizing feedback. A computationally efficient algorithm for the solution of these two coupled equations, which leads to the computation of a desired output feedback, is presented     

Robust stabilization of singular systems withH ∞-bounded uncertainty

In this paper the problem of robust stabilizing a linear, time-invariant singular system is studied. The characterization is given in terms ofH -bounded perturbations to the numerator and denominator factors of its normalized left coprime factorization. An optimal stability margin is provided in terms of the definition of the Hankel norm of a singular system. The Hankel norm is computed using two generalized Lyapunov equations.This research was supported by the Defense Advanced Research Projects Agency under contract MDA-972-93-1-0032 and MDA-972-95-3-0016.     

State feedback design using reduced-order nonsquare descriptions

A pole-placement technique is proposed for computing state feedback in multi-input linear systems. The algorithm has good numerical behavior and utilizes nonsquare pencils and the notion of decomposability. The fact that the method deals with reduced-order pencils and exploits the Schur-Hessenberg form improves the conditioning of the problem     

VLSI array processors' block implementation of IIR digital filters

VLSI systolic and wavefront array processors' architectures for the block implementation of infinite impulse response digital filters with very high sample rates are presented. The proposed systolic array processor achieves the maximum possible throughput rate and requires only local data transfers. The asynchronous wavefront array processor operates at the same maximum throughput rate and, moreover, it is characterized by a substantial reduced latency. The throughput rate of the proposed array processor structures is a linear function of the block lengthL and theoretically it may be arbitrary high; however, it is limited only by a number of practical implications.     

Finite modeling of parabolic equations using Galerkin methods and inverse matrix approximations

In this paper we examine order reduction of parabolic systems using modal truncation. The parabolic distributed system is first approximated using the Galerkin method. The system matrices have a special structure that allows us to find the approximate spectrum of the parabolic system. To do this we compute approximate inverses of tridiagonal, diagonally dominant symmetric matrices. The approximation leads to algorithms of orderO(n), as opposed to traditional algorithms of orderO(n), wheren is the order of the system. Finally, an example is presented to illustrate the proposed algorithm.This research was supported by the National Science Foundation under contract NCR-9210408, by the Advanced Research Programs Agency under contract MDA-972-93-1-0032, and by the University of Hawaii Research Council Funds.     

A bilinear formulation for the output feedback problem in linearsystems

This note ties together a geometric theory and previous algebraic results for the closed-loop eigenstructure assignment by output feedback in multivariable systems. Necessary and sufficient conditions for the closed-loop stabilization, eigenstructure assignment are presented in terms of a bilinear Sylvester equation, the solutions of which completely characterize the closed-loop eigenstructure problem with output feedback. Some preliminary results for the solution of this bilinear equation are presented     

Transmission zero assignment using semistate descriptions

The problem of finite/infinite transmission zero assignment is examined by squaring a system from the outputs to the inputs. In particular, this problem is studied in two cases: state-accessible systems and partially-state accessible systems. It is shown that the problem of transmission zero assignment for state-accessible state-variable systems is equivalent to a pole-placement problem with state feedback for a generalized system, which always has a solution. In the case of partially-state-accessible systems, it is shown that the transmission zero assignment problem is equivalent to a pole-placement problem with output feedback for a generalized system. In both cases the block Hessenberg form of the system and the extended lower triangular Hessenberg form are exploited to formulate the problem