Finite Sample Analysis of Spectral Radius Estimation and Its Applications to Networked Control Systems

The spectral radius of the system state matrix plays an important role in linear system analysis and control design. Traditional methods rely on the exact knowledge of the system matrices, from which the spectral radius can be calculated directly. Instead, we consider the setting, where one only has finitely many samples about the system input and state measurements and would like to estimate the spectral radius from these data. We provide a method for constructing an estimate of the spectral radius and derive high probability estimation error bounds. Moreover, we show how to use the estimate and the estimation error bound to assert stability criteria for networked control systems over lossy channels when only finitely many samples of system dynamics and the packet drop sequence are available.

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