COARSEST QUANTIZER DENSITY FOR QUADRATIC STABILIZATION OF TWO-INPUT LINEAR SYSTEMS

In this paper, we compute a lower bound on the coarsest quantizer density for a given quadratic Control Lyapunov Function of a two-input unstable system. The lower bound depends on the product of the magnitude of the unstable eigenvalues of the system and the selected CLF. The search over CLF’s is transformed into a problem involving one parameter on a compact set, and it is performed by gridding. We use this approach to verify that the coarsest quantizer quadratically stabilizing a twoinput linear discrete-time system has a quantization density greater than or equal to the coarsest density needed to quadratically stabilize a single input system with the same set of unstable eigenvalues.

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