Discretisation and control of polytopic systems with uncertain sampling rates and network-induced delays

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

doi:10.1080/00207179.2014.923585

Cited by 14 publications

(38 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This example was produced to highlight the application of the proposed method in the stabilization of system in form arising from a discretization procedure of a continuous‐time LPV system obtained by using a Taylor series expansion truncated at a fixed degree. In this sense, consider the continuous‐time polytopic system borrowed from Braga et al and adapted for the time‐varying case, with the following state‐space matrices:

A_{c} = ([], \begin{matrix} center \\ array 0 & array 0 & array 1 & array 0 \\ array 0 & array 0 & array 0 & array 1 \\ array - p (t) / 2 & array p (t) / 2 & array 0 & array 0 \\ array p (t) / 3 & array - p (t) / 3 & array 0 & array 0 \end{matrix}), B_{c} = ([], \begin{matrix} center \\ array 0 \\ array 0 \\ array 1 / 2 \\ array 0 \end{matrix}), C_{c} = ([], \begin{matrix} center \\ array 0.9 & array 0 & array 0 & array 0 \\ array 0 & array 0.9 & array 0 & array 0 \\ array 0 & array 0 & array 1 & array 0 \\ array 0 & array 0 & array 0 & array 1 \end{matrix}),

where p ( t ) is a parameter that can vary arbitrarily fast inside the interval 5.04 ± 1.008, yielding a polytopic LPV continuous‐time system of two vertices. In order to obtain the discrete‐time polynomial matrices A Δ ( α ) and B Δ ( α ), from , the discretization method proposed by Braga et al is used with a sampling of T = 0.6 seconds.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…As done in the proof of Theorem 1, for ease of notation, the dependence on the time-varying parameters is omitted hereafter. Knowing thatÃ cl can be written as in (22), multiplying (27) on the right by X as given in (25) and on the left by its transpose, one has…”

Section: Corollary 1 (Polytopic Lpv Systems)mentioning

confidence: 99%

“…This example was produced to highlight the application of the proposed method in the stabilization of system in form (1) arising from a discretization procedure of a continuous-time LPV system obtained by using a Taylor series expansion truncated at a fixed degree. In this sense, consider the continuous-time polytopic system borrowed from Braga et al 22 and adapted for the time-varying case, with the following state-space matrices:…”

Section: Robust Stabilization Of Lpv Systems With Norm-bounded Termsmentioning

confidence: 99%

“…where p(t) is a parameter that can vary arbitrarily fast inside the interval 5.04 ± 1.008, yielding a polytopic LPV continuous-time system of two vertices. In order to obtain the discrete-time polynomial matrices A Δ ( ) and B Δ ( ), from (44), the discretization method proposed by Braga et al 22 is used with a sampling of T = 0.6 seconds. Usually, to solve the problem of digital control of polytopic LTI or LPV continuous-time systems, some papers in the literature discretize only the vertices of the continuous-time model using a constant sampling time and a first-order Taylor approximation (also known as Euler's approximation), thus producing another polytope (ie, an affine parameter-dependent system) in the discrete-time domain.…”

Section: Robust Stabilization Of Lpv Systems With Norm-bounded Termsmentioning

confidence: 99%

“…The motivation to consider such models arises from the discretization of polytopic continuous‐time linear parameter‐varying (LPV) systems (or uncertain time‐invariant systems), which comes out with several practical applications, for example, in the context of networked control systems . Using a Taylor series expansion of arbitrary fixed degree, as proposed by Braga et al, the resulting discretized system can be represented with this particular structure. Although the discretization procedure is not investigated in this paper, this representation is adopted because it generalizes several models found in the literature.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

New robust LMI synthesis conditions for mixed gain‐scheduled reduced‐order DOF control of discrete‐time LPV systems

Rosa

Morais

Oliveira

2018

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

Summary This paper investigates the problems of stabilization and mixed H2false/H∞ reduced‐order dynamic output‐feedback control of discrete‐time linear systems. The synthesis conditions are formulated in terms of parameterdependent linear matrix inequalities (LMIs) combined with scalar parameters, dealing with state‐space models where the matrices depend polynomially on time‐varying parameters and are affected by norm‐bounded uncertainties. The motivation to handle these models comes from the context of networked control systems, particularly when a continuous‐time plant is controlled by a digitally implemented controller. The main technical contribution is a distinct LMI‐based condition for the dynamic output‐feedback problem, allowing an arbitrary structure (polynomial of arbitrary degree) for the measured output matrix. Additionally, an innovative heuristic is proposed to reduce the conservativeness of the stabilization problem. Numerical examples are provided to illustrate the potentialities of the approach to cope with several classes of discrete‐time linear systems (time‐invariant and time‐varying) and the efficiency of the proposed design conditions when compared with other methods available in the literature.

show abstract

A_{c} = ([], \begin{matrix} center \\ array 0 & array 0 & array 1 & array 0 \\ array 0 & array 0 & array 0 & array 1 \\ array - p (t) / 2 & array p (t) / 2 & array 0 & array 0 \\ array p (t) / 3 & array - p (t) / 3 & array 0 & array 0 \end{matrix}), B_{c} = ([], \begin{matrix} center \\ array 0 \\ array 0 \\ array 1 / 2 \\ array 0 \end{matrix}), C_{c} = ([], \begin{matrix} center \\ array 0.9 & array 0 & array 0 & array 0 \\ array 0 & array 0.9 & array 0 & array 0 \\ array 0 & array 0 & array 1 & array 0 \\ array 0 & array 0 & array 0 & array 1 \end{matrix}),

Section: Numerical Examplesmentioning

confidence: 99%

Section: Corollary 1 (Polytopic Lpv Systems)mentioning

confidence: 99%

Section: Robust Stabilization Of Lpv Systems With Norm-bounded Termsmentioning

confidence: 99%

Section: Robust Stabilization Of Lpv Systems With Norm-bounded Termsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

New robust LMI synthesis conditions for mixed gain‐scheduled reduced‐order DOF control of discrete‐time LPV systems

Rosa

Morais

Oliveira

2018

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network‐induced delay

Leandro¹,

Pereira

2023

Asian Journal of Control

View full text Add to dashboard Cite

This paper addresses the state derivative feedback control problem for uncertain polytopic systems subject to an uncertain sampling period and network‐induced delay. The distinctive contribution relies on the direct design of a robust state derivative feedback controller employing an augmented discretized model derived in terms of the state derivative feedback such that network‐induced delay and uncertain sampling periods can be incorporated from the original continuous‐time state‐space representation into the discretized model. Two augmented models are provided to handle longer input time delays, as well as delays less or equal to the sampling period. In this work, all the uncertain parameters are modeled as a polytopic form whose resulting discrete‐time model has matrices with polynomial dependence on the uncertain parameters and an additive norm‐bounded term featuring the discretization residual error. Moreover, synthesis conditions are derived using a set of linear matrix inequalities (LMI) to solve the stabilization problem for this class of systems under different input time delays. Finally, numerical simulations are carried out to evaluate the effectiveness of the proposed method.

show abstract

Linear quadratic networked control of uncertain polytopic systems

Braga

Morais

Tognetti

et al. 2015

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

SUMMARYThis paper investigates the problem of designing robust linear quadratic regulators for uncertain polytopic continuous-time systems over networks subject to delays. The main contribution is to provide a procedure to determine a discrete-time representation of the weighting matrices associated to the quadratic criterion and an accurate discretized model, in such a way that a robust state feedback gain computed in the discretetime domain assures a guaranteed quadratic cost to the closed-loop continuous-time system. The obtained discretized model has matrices with polynomial dependence on the uncertain parameters and an additive norm-bounded term representing the approximation residual error. A strategy based on linear matrix inequality relaxations is proposed to synthesize, in the discrete-time domain, a digital robust state feedback control law that stabilizes the original continuous-time system assuring an upper bound to the quadratic cost of the closed-loop system. The applicability of the proposed design method is illustrated through a numerical experiment.

show abstract

Discretisation and control of polytopic systems with uncertain sampling rates and network-induced delays

Cited by 14 publications

References 23 publications

New robust LMI synthesis conditions for mixed gain‐scheduled reduced‐order DOF control of discrete‐time LPV systems

New robust LMI synthesis conditions for mixed gain‐scheduled reduced‐order DOF control of discrete‐time LPV systems

On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network‐induced delay

Linear quadratic networked control of uncertain polytopic systems

Contact Info

Product

Resources

About