On Eigenvectors and Generalized Eigenvectors in Multi-Variable Descriptor Control Systems

1996 ◽  
Vol 210 (3) ◽  
pp. 183-188
Author(s):  
G P Liu ◽  
R J Patton
Keyword(s):  
Control Systems ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Eigenstructure Assignment ◽  
Singular Matrix ◽  
Linearly Independent ◽  
Generalized Eigenvectors

This paper is concerned with an eigenvector problem in multi-variable descriptor control systems. It proves that the eigenvectors and generalized eigenvectors premultiplied by the singular matrix E of the descriptor system as well as the eigenvectors and the generalized eigenvectors, which play a very important role in the design of multi-variable descriptor systems via eigenstructure assignment, are linearly independent.

scholarly journals Design of regular positive and stable descriptor systems via state-feedbacks for descriptor continuous-time linear systems with singular pencils

2014 ◽  
Vol 24 (3) ◽  
pp. 289-297
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Special Form ◽  
The State ◽  
New Method ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Asymptotically Stable ◽  
Numerical Example ◽  
Time Linear

Abstract A new method is proposed of design of regular positive and asymptotically stable descriptor systems by the use of state-feedbacks for descriptor continuous-time linear systems with singular pencils. The method is based on the reduction of the descriptor system by elementary row and column operations to special form. A procedure for the design of the state-feedbacks gain matrix is presented and illustrated by a numerical example

scholarly journals Positive Normalization of Discrete Descriptor System under Disturbance

MATEMATIKA ◽  
2018 ◽  
Vol 34 (3) ◽  
pp. 141-147
Author(s):  
Ahmad Iqbal Baqi ◽  
Admi Nazra ◽  
Zulakmal Zulakmal ◽  
Lyra Yulianti ◽  
Muhafzan Muhafzan
Keyword(s):  
Mathematical Model ◽  
Linear System ◽  
Unique Solution ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Real Problem ◽  
Sufficient Condition ◽  
Input Output ◽  
Application Field

It is well known the descriptor systems have a wide application field. Usually it appear as a mathematical model of a real problem, mainly the model that involves the input output relationship. It is well known that a descriptor linear system has an unique solution if the pencil matrix of the system is regular. However, there are some systems that are not regular. Moreover, even though the system is regular the solution can contain the noncausal behavior. Therefore, it is necessary to normalize the descriptor system so as it has well behavior. In this paper, we propose a feedback to normalize a discrete descriptor system under disturbance. Furthermore, we establish a sufficient condition in order for the discrete descriptor system under disturbance can be normalized positively.

scholarly journals Design of an Optimal Preview Controller for a Class of Linear Discrete-Time Descriptor Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Fucheng Liao ◽  
Zhihua Xue ◽  
Jiang Wu
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Original System ◽  
Simulation Method ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Equivalent Transformation ◽  
Normal System ◽  
Preview Control ◽  
Error System

The preview control problem of a class of linear discrete-time descriptor systems is studied. Firstly, the descriptor system is decomposed into a normal system and an algebraic equation by the method of the constrained equivalent transformation. Secondly, by applying the first-order forward difference operator to the state equation, combined with the error equation, the error system is obtained. The tracking problem is transformed into the optimal preview control problem of the error system. Finally, the optimal controller of the error system is obtained by using the related results and the optimal preview controller of the original system is gained. In this paper, we propose a numerical simulation method for descriptor systems. The method does not depend on the restricted equivalent transformation.

scholarly journals Finite-Time Stability Analysis for a Class of Continuous Switched Descriptor Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Pan Tinglong ◽  
Yang Kun ◽  
Shen Yanxia ◽  
Gao Zairui ◽  
Ji Zhicheng
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Time Interval ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

Finite-time stability has more practical application values than the classical Lyapunov asymptotic stability over a fixed finite-time interval. The problems of finite-time stability and finite-time boundedness for a class of continuous switched descriptor systems are considered in this paper. Based on the average dwell time approach and the multiple Lyapunov functions technique, the concepts of finite-time stability and boundedness are extended to continuous switched descriptor systems. In addition, sufficient conditions for the existence of state feedback controllers in terms of linear matrix inequalities (LMIs) are obtained with arbitrary switching rules, which guarantee that the switched descriptor system is finite-time stable and finite-time bounded, respectively. Finally, two numerical examples are presented to illustrate the reasonableness and effectiveness of the proposed results.

Design of Controller for Linear Mechanical Descriptor Systems

1994 ◽  
Vol 116 (4) ◽  
pp. 628-634 ◽  
Author(s):  
Tie-Jun Yu ◽  
P. C. Mu¨ller
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Method ◽  
Pole Assignment ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Necessary Condition ◽  
Feedback Controllers ◽  
Constrained Mechanical Systems ◽  
Quadratic Performance Index ◽  
Quadratic Performance

Mechanical descriptor systems, i.e., constrained mechanical systems, have many applications in practice. This paper studies the control of mechanical descriptor systems. First, a class of the state feedback controllers assigning the finite poles of mechanical descriptor systems at any desired locations is presented. Second, based on the degrees of freedom of pole-assignment controller, an optimization method for designing the controller that assigns the finite poles of closed-loop mechanical descriptor system and simultaneously minimizes a quadratic performance index is proposed. The necessary condition for the pole-assignment controller to be optimal is derived and the corresponding algorithms are discussed. An example is given to illustrate the validity of method in this paper.

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