Bounded Power Signal Spaces for Robust Control and Modeling
SIAM Journal on Control and Optimization
Squared and absolute errors in optimal approximation of nonlinear systems
Automatica (Journal of IFAC)
Brief Frequency response function measurements in the presence of nonlinear distortions
Automatica (Journal of IFAC)
On linear models for nonlinear systems
Automatica (Journal of IFAC)
LTI approximation of nonlinear systems via signal distribution theory
Automatica (Journal of IFAC)
Foundations of the functional approach for signal analysis
Signal Processing - Special section: Multimodal human-computer interfaces
Measuring a linear approximation to weakly nonlinear MIMO systems
Automatica (Journal of IFAC)
On robustness in control and LTI identification: Near-linearity and non-conic uncertainty
Automatica (Journal of IFAC)
Linear approximations of nonlinear FIR systems for separable input processes
Automatica (Journal of IFAC)
Separability of scalar random multisine signals
Automatica (Journal of IFAC)
| Hi-index | 22.16 |
Least-squares linear time-invariant (LTI) approximation of discrete-time nonlinear systems is studied in a generalized harmonic analysis setting extending an earlier result based on quasistationary signals. The least-squares optimal LTI model is such that the crosscorrelation between the input and the LTI model output equals the crosscorrelation between the input and the output of the nonlinear system. New results for limits of sample averages of signals are derived via Riemann-Stieltjes integration theory. These results are applied to crosscorrelation and quasistationarity analysis of input-output signals for several important classes of nonlinear systems, including stable finite memory, Wiener and Hammerstein systems. This analysis demonstrates that the assumptions used in the least-squares LTI approximation setup are fairly mild. Finally, an illustrative example is provided.