Control system performance under dynamic quantization: the scalar case

This paper derives an upper bound on the quantization error generated by a scalar quantized feedback control system. We assume a dynamic quantization policy in which feedback data is randomly dropped in accordance with an (m, k)-firm guarantee rule. Our main result identifies the minimum quantization level required to assure a specified signal-to-quantization ratio (SQR). We also show that these performance bounds scale in an exponential manner with k - m, thereby suggesting that real-time systems enforcing an (m, k)-firm guarantee rule should seek to keep k as small as possible.