Time-Invariant Dynamic Systems identification based on the qualitative features of the response

The problem of Systems Identification starts with a time-series of observed data and tries to determine the simplest model capable of exhibiting the observed behavior. This optimization problem searches the model from a space of possible models. In this paper, we present the theory and algorithms to perform Qualitative and Quantitative Systems Identification for Linear Time-Invariant Dynamic Systems. The methods described here are based on successive elimination of the components of the system's response. Sinusoidals of high frequencies are eliminated first, then their carrying waves. We continue with the process until we obtain a non-oscillatory carrier. At this point, we determine the order of the carrier. This procedure allows us to determine how many sinusoidal components and exponential components are found in the impulse response of the system under study. The number of components determines the order of the system. The paper is composed of two important parts, the statement of some mathematical properties of the responses of Linear Time Invariant Dynamic Systems, and the proposal of a set of filters that allows us to implement the recognition algorithm. We present the application of the proposed methodology to analyze and model the electrical circuits and electrical power systems.