Eric A. Butcher

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SUMMARY This paper presents a new technique for studying the stability properties of dynamic systems modeled by delay-differential equations (DDEs) with time-periodic parameters. By employing a shifted Cheby-shev polynomial approximation in each time interval with length equal to the delay and parametric excitation period, the dynamic system can be reduced(More)
We consider the problem of rendezvous, proximity operations, and docking of an autonomous spacecraft. The problem can be conveniently divided into four phases: 1) rendezvous with angles-only measurements; 2) rendezvous with angle and range measurements; 3) docking phase; and 4) docked phase. Due to the different constraints, available measurements, and(More)
This chapter provides a brief literature review together with detailed descriptions of the authors' work on the stability and control of systems represented by linear time-periodic delay-differential equations using the Chebyshev and temporal finite element analysis (TFEA) techniques. Here, the theory and examples assume that there is a single fixed(More)
In this paper, we obtain an analytical Lyapunov-based stability conditions for scalar linear and nonlinear stochastic systems with discrete time-delay. The Lyapunov– Krasovskii and Lyapunov–Razumikhin methods are applied with techniques from stochastic calculus to obtain the regions of mean square asymptotic stability in the parameter space. Both(More)
In this paper, a new efficient method is proposed to obtain the transient response of linear or piecewise linear dynamic systems with time delay and periodic coefficients under arbitrary control excitations via Chebyshev polynomial expansion. Since the time domain can be divided into intervals with length equal to the delay period, at each such interval the(More)
Chebyshev polynomials are utilized to obtain solutions of a set of pth order linear differential equations with periodic coefficients. For this purpose, the operational matrix of differentiation associated with the shifted Chebyshev polynomials of the first kind is derived. Utilizing the properties of this matrix, the solution of a system of differential(More)
— Observer-based attitude controllers for single-and multi-actuator maneuvers are developed from the delayed state feedback control laws obtained by the Lyapunov-Krasovskii functional and inverse dynamics approaches, respectively. The TRIAD algorithm is employed to process the observations. The observer gain is selected based on the extended Kalman-Bucy(More)
A technique for dimensional reduction of nonlinear delay differential equations with time-periodic coefficients is presented. The DDEs considered here have at most cubic nonlinearities multiplied by a perturbation parameter. The periodic terms and matrices are not assumed to have predetermined norm bounds, thus making the method applicable to systems with(More)