Eigenstructure Assignment In Linear Systems Research Articles

Eigenstructure assignment for linear systems with probabilistic uncertainties

In this paper, S (stochastic)-eigenvalue concept and its S-eigenvector for linear continuous-time systems with probabilistic uncertainties is proposed. The proposed concept is concerned with the perturbation of eigenvalues due to the probabilistic variable parameters in the dynamic model of a plant. S-eigenstructure assignment scheme via the Sylvester equation approach based on the S-eigenvalue concept is also proposed. The proposed design schemes are illustrated by numerical examples, and applied to the longitudinal dynamics of open-loop-unstable aircraft with possible uncertainties in aerodynamic and thrust effects as well as separate dynamic pressure. These results explicitly characterize how S-eigenvalues in the complex plane may impose stability on S-eigenstructure assignment.

A Parametric Approach for Robust Fault Detection in Linear Systems with Unknown Disturbances *

Abstract This note considers the problem of robust fault detection in multivariate linear systems with unknown disturbances, via full order state observers. By properly combining a sufficient condition for robust fault detection proposed by Patton and Chen (1991) and a result of eigenstructure assignment in linear systems proposed by Duan (1993 a), a parametric approach for robust fault detection is presented, which fully realises the idea proposed by Patton and Chen (1991). An example shows the effect of the proposed approach

Optimal Eigenstructure Assignment of Linear Systems

A versatile eigenstructure assignment method which utilizes the freedom in the modal matrix of the closed-loop system matrix and may be used in the solution of wide range optimisation problems arising in the design of multi-input continuous-time and discrete-time systems is presented. The method is applied to the pole assignment with H2 and H∞ optimisation, to the robust pole assignment and pole assignment with maximum stability radius and to the design of dynamic output compensators.

A note on "Comment on 'Eigenstructure assignment for linear systems'"

The use of output feedback for eigenstructure assignment in linear systems is studied in ibid., vol. AES-19, p.711-729 (Sept. 1983). The achievability subspace, (the subspace generating the assignable eigenvectors) is characterized in that paper. In ibid., vol.28, p.920-921 (July 1992), the authors proffer a counterexample as proof that the characterization of the achievability subspace given in the original article is not correct. The objective of this note is to show that the counterexample provided in does not contradict the characterization given in the original article, because hypotheses of this characterization are violated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Solutions of the equation AV+BW=VF and their application to eigenstructure assignment in linear systems

Two new simple, complete, analytical, and restriction-free solutions with complete and explicit freedom of the matrix equation AV+BW=VF are proposed. Here (AB) is known and is controllable, and F is in the Jordan form with arbitrary given eigenvalues. Based on the proposed solutions of this matrix equation, a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed, and two new algorithms are presented. The proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective. >

Comment on "Eigenstructure assignment for linear systems" by A.N. Andry, et al. [Aerospace control

In the above-titled paper (see ibid., vol.AES-19, p.711-729, Sept. 1983), an achievability subspace is given and used for eigenstructure assignment of linear systems with gain output feedback. The commenter shows that the achievability subspace is not generally achievable.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust eigenstructure assignment with a control design package

Eigenstructure assignment for linear systems is basically an inverse eigenvalue problem. Two possible solutions to this problem that have been implemented on the Ctrl-C commercial design package are presented. One is a least-squares approach, and the other is an iterative method. Both algorithms use singular-value decomposition and produce robust (well-conditioned) answers to the state-feedback pole-assignment problem. An example is included to assess the relative strengths of the two techniques. Both methods give well-conditioned solutions to the problems, and although the iterative design is computationally more expensive, it requires less advance information.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Recursive eigenstructure assignment in linear systems

In Arbel and Rath (1985) an iterative eigenvalue assignment algorithm was presented. This algorithm has the shortcomings of clustering most of the closed-loop eigenvalues on the real axis. A general method is given here for recursive eigenstructure assignment in linear systems. The method eliminates the shortcomings of the algorithm of Arbel and Rath. It is shown that the right and left eigenvectors of the closed-loop system matrix can be determined in terms of those of a small-dimension matrix A∗c . It is also shown that the results of Arbel and Tse (1980) are special cases of those of the proposed method. Moreover, the arbitrary parameters, beyond eigenvalue assignment, are shown to be embedded in the choice of a certain arbitrary invertible matrix S. Furthermore, computer-oriented steps are outlined for recursive eigenstructure assignment in large-scale systems. Numerical examples are worked out to illustrate the generality and feasibility of the proposed method.

Eigenstructure Assignment for Linear Systems

The use of feedback (full state, output, and constrained output) is considered as a means of shaping the transient response of linear time invariant systems. The underlying importance of the eigenstructure (eigenvalues/eigenvectors) is highlighted. Also, the important results and techniques are presented along with a brief literature review. An extensive flight control example is presented which should give direction to the application of eigenstructure assignment in diverse areas.