Parametric control of quasi-linear second-order systems with partitioned eigenstructure assignment by output feedback

In this paper, a parametric design approach for stabilizing a quasi-linear second-order system with partitioned eigenstructure assignment (PESA) is investigated through output feedback control. The PESA approach is established by partitioning the desired eigenvalue matrix into two parts to separate the associated right and left eigenvectors into a subset of the generalized eigenvectors simultaneously. A parametric controller is established by solving two second-order generalized Sylvester matrix equations, and a certain form with the desired eigenstructure can be derived with the established quasi-linear output feedback controller. Unlike the prevailing approach that assigns the entire set of generalized eigenvectors, which is difficult to satisfy a large number of complicated constraints in practical systems by the normalized pair of right and left eigenvector matrices, a subset of the generalized eigenvectors is considered. In addition, the proposed PESA approach provides less computational load and is easy to use. A numerical example and application in spacecraft rendezvous are provided to verify the numerical economy and high efficiency of the proposed approach.