Semiglobal Switched Predictor-Feedback Stabilization of Nonlinear Systems With Input Delay and State/Input Quantization

We develop a switched nonlinear predictor-feedback law that achieves semiglobal asymptotic stabilization of nonlinear systems with arbitrarily long input delay, under dynamic state/input quantization. Due to the mismatch between the (inapplicable) exact predictor state and the predictor state constructed in the presence of state quantization (or between the exact predictor-feedback law and its quantized version, in the case of input quantization), a semiglobal stabilization result is only achievable without imposing a global Lipschitzness assumption on the vector field and the nominal (for the delay-free case) feedback law (or assuming exponential stability of the delay/quantization-free system under the nominal controller). Nevertheless, the quantizer's range has to be sufficiently large, depending on the system data, the nominal feedback law, and an estimate of the size of initial conditions (to guarantee that the infinite-dimensional state of the system lies initially, and thus, it remains, within the quantizer's range). The nonlinear predictor-feedback laws developed employ quantized versions of exact predictor states in a nominal feedback law (or quantized versions of exact predictor-feedback laws), combined with a proper construction for the tunable parameter of the quantizer (the so-called ``zoom'' variable), which reduces, in a piecewise constant manner, the quantization error. The stability proofs rely on constructive derivation of solutions estimates, via a combination of input-to-state stability (ISS) arguments and backstepping transformations.