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Quantized state feedback control for multiple-input systems subject to signal-to-noise ratio constraints

This paper deals with the problem of state feedback stabilization for multiple-input discrete-time systems over communication channels, where both logarithmic quantization errors and white noises are included. The logarithmic quantizer is characterized by a received signal-to-error ratio (R-SER) model; while the white noises are modelled by additive white Gaussian noise (AWGN) channels where signal-to-noise ratio constraints are imposed. The underlying channel capacity is defined through a mixed deterministic stochastic way. The desired control law is assumed to stabilize the system with the presence of quantized errors and to satisfy some predetermined power level, simultaneously. By assuming that the overall channel capacity can be allocated among the communication channels, a solvability condition is derived in terms of Mahler measure of the plant and the desired feedback gain is given by solving some algebraic Riccati equations. An example is included to illustrate the current results.