Stabilization of Systems with Quantized Feedback and Measurements

Abstract

As we know, two quantizers are used frequently. The uniform quantizer is introduced in above chapter, as for logarithmic quantizer, wonderful results have been obtained. In [40], a logarithmic quantizer is firstly presented for stabilization of a linear discrete-time system. Ref. [51] shows an alternative proof for the optimal design and extends the results to quantized output feedback and quantized quadratic performance control using the sector bound method. Output feedback control of discrete-time linear systems using a finite-level quantizer is studied in [52]. A new approach based on sector bound method is used to analyze the stability of quantized feedback control systems in [237]. Remote control system affected by quantized signal is considered in [86]. Based on a quantization dependent Lyapunov function, the study on stability analysis of quantized feedback control system is given in [55]. The problems of discontinuous stabilization and robust stabilization of nonlinear systems are discussed in [21] and [139], respectively. Ref. [57] considers the problem of dynamic out-feedback stabilization of NCSs. In [66] and [67], the adaptive quantized control is considered and an adaptive feedback control law is given to ensure Lyapunov stable and x(k)→0 as k→ ∞. In [185], quantization and packet dropout are considered simultaneously, packet losses rate and unstable poles of the plant are considered to ensure different stability of the system, such as stochastically quadratically stable and mean square practically stable.