A new procedure for discretization and state feedback control of uncertain linear systems

Braga, Márcio F.; Morais, Cecília F.; Tognetti, Eduardo S.; Oliveira, Ricardo C. L. F.; Peres, Pedro L. D.

doi:10.1109/cdc.2013.6760901

Cited by 24 publications

(15 citation statements)

References 13 publications

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“…We make use of 100 sample points for α 1 . We can see, from Figure 2, that, even though we make use of a simple condition, we are able to get better results than the ones in [28] with = 5.…”

Section: Numerical Examplementioning

confidence: 87%

“…The aim of this example is to search the parameter space of a and b and find the region under which we are able to find a stabilizing controller. We compare the region found with the one in [28] with l = 5. We make use of 100 sample points for α 1 .…”

Section: Numerical Examplementioning

confidence: 91%

“…We present two different examples and compare their results with the ones in [28]. The methods presented here were implemented in Matlab R2016 using YALMIP [29] and Mosek.…”

Section: Numerical Examplementioning

confidence: 99%

See 2 more Smart Citations

A Tensor Product Model Transformation Approach to the Discretization of Uncertain Linear Systems

Campos¹,

Vianna²,

Braga³

2018

APH

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Most of the discretization approaches for uncertain linear systems make use of the series representation of the matrix exponential function and truncate the summation after a certain order. This usually leads to discrete-time uncertain polytopic models described by polynomial matrices with multiple indexes, which usually means that the higher the order used in the approximation, the higher the number of linear matrix inequalities (LMI) needed. This work, instead, proposes an approach based on a grid of the possible values for the matrix exponential function and an application of the tensor product model transformation technique to find a suitable polytopic model. Numerical examples are presented to illustrate the advantages and the applicability of the proposed technique.

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Section: Numerical Examplementioning

confidence: 87%

Section: Numerical Examplementioning

confidence: 91%

See 1 more Smart Citation

A Tensor Product Model Transformation Approach to the Discretization of Uncertain Linear Systems

Campos¹,

Vianna²,

Braga³

2018

APH

View full text Add to dashboard Cite

show abstract

“…Finally, in view of the product between and c in (10), the (A, B) matrices in (8) will belong to a polytope with N 2 vertices, which are associated to the cross-products between the vertices i , i = 1, 2, …, N, and c, j , j = 1, 2, …, N. An alternative uncertainty description for matrix could also be derived by taking into account higher order terms in the power series expansion of e c T , as proposed in Braga, Morais, Tognetti, Oliveira, and Peres (2013). However, the approach described herein leads to simpler design procedures and can be appropriate to meet closed loop specifications, as will be illustrated in Section 4.3.…”

Section: Remark 33 (Polytopic Uncertainties)mentioning

confidence: 99%

Direct discrete time design of robust state derivative feedback control laws

Rossi

Galvão

Teixeira

et al. 2016

International Journal of Control

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This paper is concerned with the problem of designing robust state derivative feedback control laws in discrete time. The main contribution consists of a method for recasting a continuous time state space model in the form of a discrete time model formulated in terms of the state derivative. Uncertain input delays and parametric uncertainties in polytopic form can be propagated from the original state space representation to the resulting state derivative model. Therefore, robust control techniques originally developed for discrete time state space models can be directly employed to design the state derivative feedback law. Three computational examples are presented for illustration. The first example highlights the importance of accounting for the effect of sampling in the design procedure. More specifically, a linear quadratic regulation problem involving the state derivative is addressed. The second example involves the design of a robust predictive controller in the presence of input constraints and uncertain time delay. Finally, the third example is concerned with robust pole placement in the presence of parametric uncertainty.

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“…Furthermore, it preserves the polytopic convex structure. Some authors use a Taylor series expansion of an arbitrary degree [27], but, in the case of expansion to include the high order terms, the linear correspondence above vanishes.…”

Section: Statement Of the Problemmentioning

confidence: 99%

Robust D-stability via discrete controllers for continuous time uncertain systems using LMIs with a scalar parameter

Leandro

Colombo

Kienitz

2015

2015 23rd Mediterranean Conference on Control and Automation (MED)

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This paper addresses an alternative for the synthesis of a discrete-time stabilizing controller, taking into account requirements of D-stability via Linear Matrix Inequalities (LMIs) with a certain scalar parameter. Considering continuous time systems with polytopic uncertainty, this paper contributes with an alternative to incorporate D-stability requirements in the H 2 and H ∞ discrete-time controller synthesis from continuous-time D-stable regions via Euler's approximation. From these design requirements, robust controllers were designed and implemented for a case study system of two cars connected through a spring.

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A new procedure for discretization and state feedback control of uncertain linear systems

Cited by 24 publications

References 13 publications

A Tensor Product Model Transformation Approach to the Discretization of Uncertain Linear Systems

A Tensor Product Model Transformation Approach to the Discretization of Uncertain Linear Systems

Direct discrete time design of robust state derivative feedback control laws

Robust D-stability via discrete controllers for continuous time uncertain systems using LMIs with a scalar parameter

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