Search

In this paper, we discuss the minimal positive realizations for nth-order rational transfer function of a discrete time-invariant linear single-input-single-output (SISO) system with negative poles. By the constructive method, the necessary and sufficient conditions are provided for these transfer functions to have a positive realization of dimension n. With the benefit of these results, an improvement is made on the existing results about the positive decomposition problem in positive system theory. Numerical examples are employed to validate the results.

This paper analyzes when a Hopf bifurcation occurs for a class of delay differential systems, and constructs the algorithms for determining the bifurcation's occurrence. By using some algebraic criteria, the "complete discrimination system for polynomials" and Hurwitz criterion, on-line determining bifurcation's occurrence can be realized. The methods unify and generalize the relevant results in the literature.

The estimation of frequencies and amplitude of sinusoids in noise has many applications in various fields such as fault diagnosis, communications, radar, sonar, and so on. Many algorithms are available to estimate the frequencies of sinusoids either in white noise or in colored noise. This paper is mainly concerned with the estimation of the amplitude of a sinusoid with high resolution in white noise in case of knowing its frequency. The algorithm is suitable not only for stochastic process, but also for deterministic process. To compare effectiveness of the algorithm with that of other estimators, two simulation examples are presented to estimate the amplitudes of sinusoids in white noise with elliptic filter and the algorithm given in this paper. The algorithm is also testified in estimation of the sinusoid's amplitude at some frequency in a fuel cell system.