This paper reviews and compares the computational cost of several methods to analytically obtain the natural response of linear time-invariant (LTI) circuits. In particular, the analysis is focused on three methods: eigensystem-based procedure, Vandermonde matrix method and Lagrange interpolation formula. The computational cost of repeated solutions, in which only the initial conditions change, is also studied. Finally, the computational cost of the eigensystem-based approach, the winner of the analytical class of methods, is compared with that of the numerical integration approach for different number of integration steps and scenarios.

Based on several new Lyapunov–Krasovskii functionals, by employing the homeomorphism mapping principle, the Halanay inequality, a nonlinear measure approach and linear matrix inequality (LMI) techniques, several delay-independent sufficient criteria are obtained for the existence, uniqueness and globally exponential stability of considered neural networks. Without assuming the boundedness and monotonicity of activation functions, the obtained conditions generalize some previous results in the literature. Two examples are also given to show the less conservativeness of the obtained conditions.

An efficient envelope analysis based on the harmonic balance method has been proposed. Since the determining equation of the HB method is given by the schematic diagram, our method can be easily applied to many kinds of circuits. From many simulation experiments, it has been found that our envelope analysis is about fifty times faster than the direct transient analysis.