Robust State‐Derivative Feedback LMI‐Based Designs for Linear Descriptor Systems

Faria, Flávio A.; Assunção, Edvaldo; Teixeira, Marcelo Carvalho Minhoto; Cardim, Rodrigo

doi:10.1155/2010/927362

Cited by 28 publications

(19 citation statements)

References 33 publications

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“…It satisfies item (i) of Finsler's Lemma, then there is a matrix = > 0, accomplishing the Lyapunov conditions for system (2), taking into account the gain matrices (12), then system (5) is asymptotically stable. Figure 1 shows a set D for allocating the eigenvalues of the system.…”

Section: Theorem 2 Assuming Is Invertible If There Exist Symmetric mentioning

confidence: 99%

“…Some researchers have sought to develop methods similar to those existing for the state vector feedback; for example, [1] developed a formula similar to the widespread Ackerman for linear systems (SISO) through derivative feedback. In [2], a new formulation was presented for the stabilization of linear multivariable systems under derivative feedback states. In [3], an analysis was presented of linear systems of observability and stability through the state vector derived and a study on the disturbance rejection with state derivative feedback.…”

Section: Introductionmentioning

confidence: 99%

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Design of Gain Scheduling Control Using State Derivative Feedback

Llins

Assunção

Teixeira

et al. 2017

Mathematical Problems in Engineering

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In recent years, the study of systems subject to time-varying parameters has awakened the interest of many researchers. The gain scheduling control strategy guarantees a good performance for systems of this type and also is considered as the simplest to deal with problems of this nature. Moreover, the class of systems in which the state derivative signals are easier to obtain than the state signals, such as in the control for reducing vibrations in a mechanical system, has gained an important hole in control theory. Considering those ideas, we propose sufficient conditions via LMI for designing a gain scheduling controller using state derivative feedback. The D-stability methodology was used for improving the performance of the transitory response. Practical implementation in an active suspension system and comparison with other methods validates the efficiency of the proposed strategy.

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Section: Theorem 2 Assuming Is Invertible If There Exist Symmetric mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design of Gain Scheduling Control Using State Derivative Feedback

Llins

Assunção

Teixeira

et al. 2017

Mathematical Problems in Engineering

Self Cite

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“…Thus Theorem 4.1 was proposed in order to limit the norm of K (Assunção et al, 2007c;Faria et al, 2010). …”

Section: Optimization Of the K Matrix Norm Of The Closed-loop Systemmentioning

confidence: 99%

“…This way expecting to find, for some situations, controllers with lower gains, thus being easier to implement than those designed using the existing quadratic stability theory (Faria et al, 2010), avoiding the signal control saturations.…”

Section: Optimization Of the K Matrix Norm Using Finsler's Lemmamentioning

confidence: 99%

“…Some difficulty in applying the existing theorem (Faria et al, 2010) was found to the new structure of LMIs, as the controller synthesis matrix Y is not symmetric, a condition that was necessary for the development of Theorem (4.1) when the controller synthesis matrix was X = P −1 . Thus, Theorem 5.3 is proposed.…”

Section: Optimization Of the K Matrix Norm Using Finsler's Lemmamentioning

confidence: 99%

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New Techniques for Optimizing the Norm of Robust Controllers of Polytopic Uncertain Linear Systems

Buzachero¹,

Assunção²,

Teixeira³

et al. 2012

Frontiers in Advanced Control Systems

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Robust stability and stabilization for descriptor systems with uncertainties in all matrices

Cheng

Zhang

2017

Intl J Robust & Nonlinear

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Summary This paper is concerned with the robust stability and stabilization via state feedback for a class of continuous linear time‐invariant descriptor systems with norm‐bounded perturbations in derivative matrix E and other systems matrices A and B. Due to the fact that matrix E being rank invariant is an efficient necessary condition to the solvability of stabilization via state feedback, perturbations in matrix E can be described in a new form that is different from the general form studied in previous works. Problems under consideration fall into 2 cases, ie, one is expressed by a constant matrix left multiplying an invertible uncertain matrix, and the other is produced by a dual form of the first case. Then, we transfer the problem of robust stability into the question of a feasible solution for linear matrix inequality and necessary and sufficient conditions for stability are derived for the 2 cases. In terms of the stabilization problem, by using a new state augmentation technique, we transfer the descriptor system with uncertainties in the derivative matrix into an augmented descriptor system that the derivative matrix has no uncertainties, and we find that there are no properties changed during this augmentation process. Next, basing on the theory of stability, we receive sufficient conditions to the original stabilization problem for the 2 cases. Finally, 2 numerical examples are given to illustrate the effectiveness and merits of the main results.

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Robust State‐Derivative Feedback LMI‐Based Designs for Linear Descriptor Systems

Cited by 28 publications

References 33 publications

Design of Gain Scheduling Control Using State Derivative Feedback

Design of Gain Scheduling Control Using State Derivative Feedback

New Techniques for Optimizing the Norm of Robust Controllers of Polytopic Uncertain Linear Systems

Robust stability and stabilization for descriptor systems with uncertainties in all matrices

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