Robust controller design ensuring the desired aperiodic stability degree of a control system with affine uncertainty

This paper considers a system whose characteristic polynomial coefficients are linear combinations of the interval parameters of a plant forming a parametric polytope. A linear robust controller is parametrically designed to place a dominant pole of the system within the desired interval of the negative real semi-axis and ensure an aperiodic transient in the system. The parametric design procedure involves a low-order controller with dependent and free parameters: the former serve to place the dominant pole within the desired interval on the complex plane whereas the latter to shift the other poles to some localization regions beyond a given bound (to the left of the dominant pole to satisfy the pole dominance principle). To evaluate the dependent parameters of the controller, the originals of the interval bounds of the dominant pole are determined for the plant's parametric polytope based on a corresponding theorem (see below). The free parameters of the controller are chosen using the robust vertex or edge $D$-partition method, depending on the boundary edge branches of the localization regions of the free poles. A numerical example of the parametric design procedure is provided: a PID controller is built to ensure an acceptable aperiodic transient time in a load-lifting mechanism with interval values of cable length and load weight.