Minimization of the worst-case steady-state error for multivariable. Deadbeat control systems with time-varying uncertainty

This paper presents a simple design method for obtaining multivariable deadbeat controllers minimizing the worst-case effect of time-varying norm-bounded unstructured uncertainty on the steady-state controlled error under guaranteeing the robust stability of the system. The contributions are the following. First, for a given linear time-invariant multivariable system, the worst-case perturbation that maximizes the effect on the steady-state controlled error is derived in a class of time-varying norm-bounded perturbations. Consequently, the worst-case steady-state controlled error is presented in an explicit form. Secondly, the minimization problem is reduced to a linear programming problem. Therefore the proposed design method is simple and straightforward. Thirdly, the design method does not require some troublesome assumptions imposed in the previous results on the plant and the weighting function of perturbation.