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- Eric A. Butcher, Haitao Ma, Ed Bueler, Victoria Averina, Zsolt Szabo
- 2004

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)

This work reports new approaches for order reduction of nonlinear systems with time periodic coefficients. First, the equations of motion are transformed using the Lyapunov-Floquet (LF) transformation, which makes the linear part of new set of equations time invariant. At this point, either linear or nonlinear order reduction methodologies can be applied.… (More)

- Eric Butcher, Brian Mann
- 2008

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)

- Amit K. Sanyal, Maziar Izadi, Eric A. Butcher
- ACC
- 2014

— 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)

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)

Some new techniques for reduced order (macro) modeling of nonlinear systems with time periodic coefficients are discussed in this paper. The dynamical evolution equations are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the new set of equations become time-invariant. The techniques presented here reduce the order… (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)