State-space identification of switching linear discrete time-periodic systems with known scheduling signals

Abstract

In this paper, we propose a novel frequency domain state-space identification method for switching linear discrete time-periodic (LDTP) systems with known scheduling signals. The state-space identification problem of linear time-invariant (LTI) systems has been widely studied both in the time and frequency domains. Indeed, there have been several studies that also concentrated on state-space identification of both continuous and discrete linear time-periodic (LTP) systems. The focus in this study is the family of LDTP systems that switch among a finite set of subsystems triggered by known periodic scheduling signals. We address the state-space identification of such systems in frequency domain using input-output data. We also assume that full state measurements are available for the identification process.The major difference of our study is that we explicitly model the known scheduling signals responsible for switching, which greatly reduces the parametric complexity as well as potentially increases the estimation accuracy by avoiding overfitting. In our identification framework, we gather the Fourier transformations of input-output data, known periodic scheduling signals, and state-space system dimensions and fuse them in a linear regression framework. Later, we estimate the Fourier series coefficients of the time-periodic system and input matrices using a least-squares solution. Finally, we illustrate the effectiveness of our method using a switching LDTP system that is based on the damped Mathieu equation.