Quantized linear systems (Q2724380)

Linear time-invariant discrete-time systems are considered. It is assumed that the systems are stabilizable. The main goal is to develop a theory of stabilization for the systems by using only a quantized input. In the first part of the paper the number of input values is assumed to be countable. A quantized state-feedback controller is derived by introducing a quadratic Lyapunov function. It is shown that the quantizer follows a logarithmic law. A coarsest quantizer over all quadratic control Lyapunov functions is derived by solving a Riccati equation.NEWLINENEWLINENEWLINEThe derived methods can be used for developing state estimators using a countable number of measurements. The state estimator is used for developing quantized output controllers. The results are extended to discrete-time systems obtained from sampled continuous linear time-invariant systems. An optimal sampling time that minimizes the density of control or measurement values is derived. In the second part finite quantizers are investigated. It is shown that the system can be stabilized by truncating the logarithmic quantizer.NEWLINENEWLINENEWLINEThe results are illustrated by a numerical example.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00036].