Linear‐quadratic parametrization of stabilizing controls in discrete‐time 2D systems

This paper considers a class of linear discrete‐time 2D systems in the form of repetitive processes with uncertain parameters. Using LQR theory ideas a parametric description of stabilizing controls via output feedback is developed, which leads to the development of efficient LMI‐based algorithms for computation of the gain matrix. The results are extended to repetitive processes with Markovian jumps, and a numerical example is given to demonstrate the application of the algorithm developed to the synthesis of stabilizing control laws.