Robust Eigenstructure Assignment For Linear Descriptor Systems Via Output Feedback

Eigenstructure assignment problem is one of the important problems in control system design. Eigenstructure assignment design is the synthesis of pole assignment design and eigenvector design, which is more able to grasp the characteristics of systems. Since Moore first proposed the concept of eigenstructure in 1976, it has been widely studied.We take the linear descriptor system as the research object. We study the problem of robust eigenstructure assignment for descriptor linear systems via output feedback.The main results are as follows:I. We propose the design method for robust eigenstructure assignment in descriptor linear systems via output feedback. Firstly, through perturbation analysis of the closed-loop eigenstructure assignment equation and based on a criterion for minimizing the closed-loop eigenstructure assignment conditions error, we propose a objective function which measures sensitivity of closed-loop eigenstructure of the systems subject to system parameter perturbations. Next, by using the solution of eigenstructure assignment in the literature we obtain the explicit parametric form of the objective function. Using this result, we transform the problem of robust eigenstructure assignment via output feedback into a constrained minimization problem of objective function.II. We give two algorithms for the robust eigenstructure assignment in descriptor linear systems via output feedback under the condition that the poles can be arbitrarily assigned, which has been proposed in the literature. Firstly, through analyzing and solving the constraint conditions, we transform the constrained minimization problem into a new unconstrained minimization problem. Secondly, we give the explicit parametric expression of the gradient of the objective function of the unconstrained minimization problem. Finally, using gradient-based optimization algorithm, we minimize the objective function. The proposed algorithms are simple, effective, and make use of all the degrees of freedom in the systems, thus they can give control systems with better robustness. Numerical examples show the effectiveness of the proposed algorithms.