Parametric control to a type of descriptor quasi‐linear systems based on dynamic compensator and multi‐objective optimisation

This study investigates the parametric approach for a type of descriptor quasi‐linear systems by utilising dynamic compensator and multi‐objective optimisation. Based on the solutions of generalised Sylvester matrix equation, the generally parameterised expressions of dynamic compensator and the left and right eigenvector matrices are both established, meanwhile, a group of arbitrary parameters are obtained. With the parametric approach, the closed‐loop system can be transformed into a linear time‐invariant one with an expected eigenstructure by using a group of canonical matrix pairs. Simultaneously, it also presents a novel technique to design multi‐objective optimisation for descriptor quasi‐linear systems. Multiple performance indexes such as low sensitivity, disturbance attenuation, robustness degree, and low gains are formulated by arbitrary parameters. Based on the above indexes, robustness criteria and low gain criteria can be expressed by a synthetic objective function which includes each performance index weighted. By utilising the degrees of freedom in arbitrary parameters, a dynamic compensator can be obtained by solving a multi‐objective optimisation problem. Finally, two examples are proposed to prove that the parametric approach is effective.