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Further results on output tracking for a class of uncertain high-order nonlinear time-delay systems

Alimhan Keylan, Kalimoldayev Maksat N., Adamov Abilmajin A., Mamyrbayev Orken, Tasbolatuly Nurbolat, Smolarz Andrzej

Przegląd Elektrotechniczny

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2019

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R. 95, nr 5

88--91

EN

This paper investigates the problem of global practical output tracking by state feedback for a class of uncertain high-order nonlinear timedelay systems. Further, we design a homogeneous state feedback controller with an adjustable scaling gain, under mild conditions on the system nonlinearities involving time delay. Through the use of a homogeneous Lyapunov-Krasovskii functional method, the scaling gain is adjusted to dominate the time-delay nonlinearities bounded by homogeneous growth conditions and render the tracking error can be made arbitrarily small while all the states of the closed-loop system remain to be bounded.

PL

W artykule opisano problem globalnego praktycznego śledzenia wyjścia za pomocą sprzężenia zwrotnego od stanu dla klasy niepewnych nieliniowych układów opóźniających wysokiego rzędu. Ponadto zaprojektowany został jednorodny kontroler sprzężenia od stanu z regulowanym wzmocnieniem skali, przy łagodnej nieliniowości i opóźnieniu czasowym. Dzięki zastosowaniu jednorodnej metody funkcjonalnej Lapunowa-Krasowskiego, wzmocnienie skali jest przystosowane do dominacji nieliniowości opóźnienia czasowego ograniczonej przez jednorodne warunki wzrostu i powoduje, że błąd śledzenia może być dowolnie mały, podczas gdy wszystkie stany systemu ze sprzężeniem zwrotnym pozostają ograniczonye.

2

Observer-based fault estimation for linear systems with distributed time delay

Filasova A., Gontkovič D., Krokavec D.

Archives of Control Sciences

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2013

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Vol. 23, no. 2

169--186

EN

The paper is engaged with the framework of designing adaptive fault estimation for linear continuous-time systems with distributed time delay. The Lyapunov-Krasovskii functional principle is enforced by imposing the integral partitioning method and a new equivalent delaydependent design condition for observer-based assessment of faults are established in terms of linear matrix inequalities. Asymptotic stability conditions are derived and regarded with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. Simulation results illustrate the design approach, and demonstrates power and performance of the actuator fault assessment.

3

Observer-based controller design of time-delay systems with an interval time-varying delay

Thuan M. V., Phat V. N., Trinh H.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 4

921-927

EN

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed \alfa-convergence rate. The design of an observer based output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.

4

LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

Balasubramaniam P., Lakshmanan S., Rakkiyappan R.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 2

339-351

EN

This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.

5

LMI based control design for linear systems with distributed time delays

Filasova A., Gontkovič D., Krokavec D.

Archives of Control Sciences

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2012

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Vol. 22, no. 2

217-231

EN

The paper concerns the problem of stabilization of continuous-time linear systems with distributed time delays. Using extended form of the Lyapunov-Krasovskii functional candidate, the controller design conditions are derived and formulated with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. The result give sufficient condition for stabilization of the system with distributed time delays. It is illustrated with a numerical example to note reduced conservatism in the system structure.