Closed-loop Eigenstructure Assignment Research Articles

Robust Flight Control Design With Eigenstructure Assignment

Although the H∞ control method is a powerful tool to design robust controller, it is difficult to attain the performances in time domain. A new design method of H∞ state feedback controller is proposed which guarantees the robust stability and assigns eigenstructure in the desired regions. Conditions of robust stability and closed loop eigenstructure assignment are solved in LMI form with one nonlinear constraint. This method is validated with numerical example of flight control design.

A bilinear formulation for the output feedback problem in linear systems

This note ties together a geometric theory and previous algebraic results for the closed-loop eigenstructure assignment by output feedback in multivariable systems. Necessary and sufficient conditions for the closed-loop stabilization, eigenstructure assignment are presented in terms of a bilinear Sylvester equation, the solutions of which completely characterize the closed-loop eigenstructure problem with output feedback. Some preliminary results for the solution of this bilinear equation are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Parametric eigenstructure assignment by output-feedback control: the case of multiple eigenvalues

This paper deals with closed-loop eigenstructure assignment by output-feedback control in linear multivariable systems for the general case of multiple eigenvalues. The approach is algebraic in nature and operates directly on the closed-loop characteristic equation using fundamental properties of determinants and their derivatives. A compact form for the controller gain matrix is derived and expressed in terms of a set of parameter vectors that specify the non-uniqueness of the solution of the eigenvalue-assignment problem. Some of these parameter vectors assume restricted forms while others are free. A computational scheme is given in which the free parameter vectors are determined in such a way as to assign the corresponding eigenvectors and generalized eigenvectors in a weighted least-square-error sense. An illustrative numerical example is included.

Eigenstructure assignment by output feedback in descriptor systems

Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback inlinear time-invariant descriptor systems are presented. These generalise in a natural way the known corresponding results for state-space systems. However, our arguments extend somewhat existing work on eigenstructure assignment by state feedback in descriptor systems. The main issue throughout the paper is closed-loop regularity, i.e. uniqueness of solutions of the initial value problem, which cannot be taken for granted.

Eigenvalue-generalized eigenvector assignment by output feedback

This note generalizes the previous results of the closed-loop eigenstructure assignment via output feedback in linear multivariable systems. Necessary and sufficient conditions for the closed-loop eigenstructure assignment by output feedback are presented. Some known results on entire eigenstructure assignment are deduced from this result.

Some necessary and sufficient conditions for eigenstructure assignment

Abstract Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback in time-invariant linear multivariable control systems are presented. A simple condition on a square matrix necessary and sufficient for it to be the closed-loop plant matrix of a given system with some output feedback is the basis of the paper. Some known results on entire eigenstructure assignment are deduced from this. The concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors.

Eigenstructure assignment in linear multivariable systems--A parametric solution

This paper generalizes a recently reported method [1] of closed-loop eigenstructure assignment via state feedback in a linear multivariable system (with n states and r control inputs). By introducing a lemma on the differentiation of determinants, the class of assignable eigenvectors and generalized eigenvectors associated with the assigned eigenvalues is explicitly described by a complete set of n r -dimensional free parameter vectors. This parametric characterization conveniently organizes the nonuniqueness of the solution of the eigenvalue-assignment problem and thereby provides an efficient means of further modifying the system dynamic response. A numerical example is worked out to demonstrate the feasibility of the method.

Dead-beat control of linear discrete-time systems

The paper considers the problem of determining the various classes of state-feed back dead-beat controllers for linear multivariable discrete-time systems. Unlike earlier work, attention is not restricted to the special case of minimum-time dead-beat controllers. A general dead-beat control problem is posed and solved. The solution is based principally on an approach of closed-loop eigenstructure assignment. The minimum of free parameters in each class are specified and used in an explicit parametric form for the feedback gain matrix. The concept of the greatest minimum of free parameters is introduced. Finally, the method is illustrated by a numerical example

Closed-loop eigenstructure assignment by state feedback in multivariable linear systems with slow and fast modes

It is shown that the recent results of Moore (1976) and Porter and D'Azzo (1977) can be readily extended so as to provide a computationally attractive method of closed-loop eigenstructure assignment by state feedback in multivariable systems with ‘ slow ’ and ‘ fast ’ modes. The general results are illustrated by designing a state-feedback controller for a third-order system with ‘ slow ’ and ‘ fast ’ modes which assigns asymptotically the entire closed-loop eigenstructure as characterized by both ‘ slow ’ and ‘ fast ’ eigenvalues and eigenvectors.

Algorithm for closed-loop eigenstructure assignment by state feedback in multivariable linear systems

Abstract In this paper an algorithm is presented which greatly facilitates the complete exploitation of state feedback in the assignment of the entire closed-loop eigenstructure of controllable multi-input systems. This algorithm is a generalization of the algorithm of MacLane and Birkhoff (1968) for the computation of a basis for the null space of a matrix and is ideally suited to digital computer implementation. The algorithm readily yields the vectors which are required (Porter and D'Azzo 1978) for the simultaneous assignment of Jordan canonical forms, eigenvectors, and generalized eigenvectors to the plant matrices of closed-loop controllable multivariable linear systems. The effectiveness of the algorithm is illustrated by assigning the entire closed-loop eigenstructure of a third-order two-input discrete-time system in such a way that the resulting closed-loop system exhibits time-optimal behaviour.

Closed-loop eigenstructure assignment by state feedback in multivariable linear systems

In this paper, results are presented which facilitate the complete exploitation of state feedback in the assignment of the entire closed-loop eigenstructure of multivariable linear systems. These results provide a method for the direct computation of the state-feedback matrix which assigns prescribed Jordan canonical forms, eigenvectors, and generalized eigenvectors to the plant matrices of closed-loop systems. This method is illustrated by assigning the entire closed-loop eigenstructure of a third-order two-input discrete-time system in such a way that the resulting closed-loop system exhibits finite settling time behaviour.