Approximation of the sampled-data linear quadratic control systems by the bilinear transformation

This paper is concerned with the digital implementation of the linear quadratic controller in the case of the sampled-data system. By applying the bilinear transformation, a way of computing a stabilizing suboptimal digital controller which does not require the resolution of the discrete Riccati equation is proposed. Corresponding values of the optimal and suboptimal discrete-time cost functions are estimated with respect to the sampling period and the degradation is evaluated. A simple numerical example is given to support the theoretical results