Eigenstructure Assignment for Linear Systems with Constraints on Input and Its Rate via State Feedback - A Parametric Approach

A parametric approach for eigenstructure assignment for linear systems with constraints on input and its rate via state feedback is proposed. Based on the parametric solution to a Sylvester matrix equation, parameterizations of all the state feedback control matrices and the closed-loop eigenvector matrices are established in a group of parameters. The positive invariance condition can be inverted into constraints on the group of parameters. Under such state feedback controller, the trajectories of the input and its rate remain in a positively invariant set. The parametric method offers more the design degrees of freedom, which can be utilized to achieve certain desired properties and performances in the design of control systems. Two numerical examples show the effect of the proposed approach