Estimation of the Transition Time of Piecewise Linear Systems by Using Wavelet Analysis

Abstract

This paper proposes an estimation method of the transition time of hybrid systems in piecewise linear (PWL) form by using wavelet analysis. If each transition time is known, the continuous dynamics between adjacent discrete transitions will be identified by conventional identification method for continuous systems. The discrete transition is represented as a switching of differential equations or a jump of continuous states. These changes can be detected as characteristic patterns in wavelet transform of an output signal. First, detectability of the discrete transition is defined and its necessary and sufficient condition is derived. Under the assumption of the detectability of the discrete transition, an output signal is represented by using Taylor expansion around the transition time. In addition, the characteristic patterns in the wavelet transform of an output signal are analyzed. An estimation method of the transition time based on the analyzed pattern is proposed. Finally, the effectiveness of the proposed method is illustrated by numerical examples.