The principles of calculus of variations are used to obtain necessary conditions for optimal control of dynamical systems that involve nonconstant time lags. Consideration is given to systems that can be represented mathematically by a finite set of ordinary nonlinear differential-difference equations with one or more time-dependent argument lags. Application of the general results to classes of linear systems with finite-time quadratic performance criteria is considered in detail. Optimal feedback control laws are given. Discussion of a proposed method for obtaining computational solutions for nonlinear systems with variable delays is included in the paper.

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A method for the determination of the domain of asymptotic stability of second-order nonlinear systems is presented. The essence of the method is the construction of Liapunov-like functions. Several simple but important examples illustrate the application of the method.

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