Iterative learning control design based on state observer

Linear control systems operating in a repetitive mode with a constant period and returning each time to the initial state are considered. The problem is to find a control law that will employ information about the output variable at the current and previous repetitions and also the estimates of state variables from an observer in order to guarantee the convergence of this variable to a reference trajectory under unlimited increasing the repetitions number. This type of control is known as iterative learning control. The problem is solved using the dissipativity of 2D models and the divergent method of vector Lyapunov functions. The final results are expressed in the form of linear matrix inequalities. An example is given.