Qualitative systems identification for linear time invariant dynamic systems

Abstract

The problem of Systems Identification starts with a timeseries 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 traditional methods, the search space is the set of numerical values to be assigned to parameters. In our approach we are constrained, and therefore limit the search space, to Linear Time-Invariant models. In this paper, we present the theory and algorithms to perform Qualitative 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 nonoscillatory carrier. At that point, we determine the order of the carrier. This procedure allows us to determine how many sinusoidal components, and how many 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.