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
Robust input-output stabilization on Z for persistent signals
Automatica (Journal of IFAC)
Squared and absolute errors in optimal approximation of nonlinear systems
Automatica (Journal of IFAC)
Robust output feedback stabilization via risk-sensitive control
Automatica (Journal of IFAC)
On linear models for nonlinear systems
Automatica (Journal of IFAC)
Brief Linear quadratic control revisited
Automatica (Journal of IFAC)
Least-squares LTI approximation of nonlinear systems and quasistationarity analysis
Automatica (Journal of IFAC)
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The nonlinear space of signals allowing Wiener's generalized harmonic analysis (GHA), the linear bounded power signal spaces of Beurling, Marcinkiewicz, and Wiener, and a new linear bounded power space are studied from a control and systems theory perspective. Specifically, it is shown that the system power gain is given by the $H_\infty$ norm of the system transfer function in each of these spaces for a large class of (power) stable finite and infinite dimensional systems. The GHA setup is shown to possess several limitations for the purpose of robustness analysis which motivates the use of the other more general (nonstationary) signal spaces. The natural double-sided time axis versions of bounded power signal spaces are shown to break the symmetry between Hardy space $H_\infty$ methods and bounded power operators; e.g., the system transfer function being in $H_\infty$ does not imply that a causal-linear time-invariant (LTI) system is bounded as an operator on any of the double-sided versions of the studied bounded power signal spaces.