Delay-Independent Stability Conditions for Some Classes of Nonlinear Systems

Aleksandrov, A. Yu.; Hu, Guang‐Da; Zhabko, Alexey P.

doi:10.1109/tac.2014.2299012

Cited by 50 publications

(23 citation statements)

References 26 publications

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“…and A a , B a are the same as in (12). The following theorem yields a controller that ensures the existence of an ISS Lyapunov function for the forced uncertain system in (23).…”

Section: 1cmentioning

confidence: 99%

“…where K M a ¼ 1, c M a ¼ 1 and Ka 2 M a ¼ 0:6: The system matrices as in (23) are obtained, by choosing the states y and _ y as x 1 and x 2 , respectively, and are given The output here is state x 1 and it is seen to track the reference input.…”

Section: Examplementioning

confidence: 99%

“…The paradigm of Lyapunov stability for the unforced states xðt; x 0 Þ, (x 0 being the initial states) has to be shifted to accommodate bounded input bounded state stability, or namely, input state stability (ISS). Interconnected systems [16][17][18] and time delay system [19][20][21][22][23] have already been stabilized on the basis of ISS, but similar applications are not found in the field of tracking of Lipschitz nonlinear systems. The proposed LMI-based method checks for the existence of an ISS Lyapunov function for the nonlinear system.…”

Section: Introductionmentioning

confidence: 99%

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LMI-based robust tracking of a class of MIMO nonlinear systems

Mukherjee

Sengupta

2019

Sādhanā

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Reference tracking problem for MIMO Lipschitz nonlinear systems is examined here. Presently a vast literature exists on observer design of unforced systems containing Lipschitz nonlinearities. However, these existing results cannot be readily extended for controller design containing reference tracking ability. Here a Linear State Variable Feedback (LSVF) controller is designed for MIMO Lipschitz nonlinear systems with norm-bounded parametric uncertainties using the concept of input to state stability Lyapunov functions. The whole problem is cast into a framework of Linear Matrix Inequalities, to exploit its numerical capabilities. Analytical proofs are supplemented with simulation examples, which show certain advantages over existing results. Apart from state feedback, observer-based output feedback is also considered for controller design.

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“…and A a , B a are the same as in (12). The following theorem yields a controller that ensures the existence of an ISS Lyapunov function for the forced uncertain system in (23).…”

Section: 1cmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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LMI-based robust tracking of a class of MIMO nonlinear systems

Mukherjee

Sengupta

2019

Sādhanā

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“…In this article, we use the methodology of Lyapunov-Krasovskii functional to analyze the stability of a class of homogeneous differential-difference systems of neutral type. It is proved that if the corresponding homogeneous system with zero delays is asymptotically stable, then the trivial solution of a homogeneous retarded type system is also asymptotically stable for any limited delays [6], [7]. Basing on these results and results [8]- [11], we constructed the complete type Lyapunov-Krasovskii functional, which are suitable for analysis of every system within the class under consideration.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Ships’ Movement Along Optimal Routes

Александрова

Zhabko

2019

WIT Transactions on the Built Environment

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In this report, we consider the system of difference-differential equations of neutral type with homogeneous, of the larger unit order, right-hand sides. The following fact is well known. If a system of retarded-type difference-differential equations with homogeneous, of the larger unit order, righthand sides is asymptotically Lyapunov stable at zero delays, then the zero solution of the initial system is also asymptotically Lyapunov stable for any continuous and bounded delays. For this case, the Lyapunov-Krasovskii functional is constructed to estimate the asymptotic stability domain of the zero solution. For a linear system of neutral type, the concept of the Lyapunov matrix is introduced and the Lyapunov-Krasovskii functional is constructed. This functional was then used to analyze exponential stability. This paper presents sufficient conditions for asymptotic Lyapunov stability and Lyapunov instability of the zero solution for a class of homogeneous difference-differential systems of neutral type. In addition, a constructive algorithm for checking the stability and instability of the zero solution is formulated. Another result is the development of a method for constructing a complete type Lyapunov-Krasovskii functional, previously used for the analysis of homogeneous differencedifferential systems of retarded type.

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“…The earlier type is independent of delay size; and is generally conservative, especially when a delay is small. On the other hand, studies of delay-dependent criteria have focused mainly on identical delays in neutral and discrete terms (Aleksandrov, Hu, & Zhabko, 2014;Lu, Wu, & Bai, 2014;Yang, Wang, & CONTACT Mohammad Karimi hmohammad.karimi021@gmail.com Wang, 2017). Sun, Liu, and Chen (2009) studied the delaydependent stability and stabilization criteria for neutral systems with time delays.…”

Section: Introductionmentioning

confidence: 99%

Further results on robust H_∞ control design for uncertain time-delay systems with actuator delay: application to PMSG machine

Karimi

2018

Systems Science & Control Engineering

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The problem of robust H ∞ state-feedback control design for a class of uncertain systems with two different time delays in the state vector and the input signal is investigated in this paper. The main feature of the paper is to develop a robust H ∞ controller, which ensures the robust asymptotic stability of the system as well as the desired H ∞ performance. By constructing a Lyapunov-Krasovskii functional, some sufficient conditions for the existence of the H ∞ state-feedback controller is derived in terms of linear matrix inequalities. Numerical examples such as a wind energy conversion system model based on a permanent magnet synchronous generator model are provided to illustrate the effectiveness of the proposed method. ARTICLE HISTORY

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Delay-Independent Stability Conditions for Some Classes of Nonlinear Systems

Cited by 50 publications

References 26 publications

LMI-based robust tracking of a class of MIMO nonlinear systems

LMI-based robust tracking of a class of MIMO nonlinear systems

Stability Analysis of Ships’ Movement Along Optimal Routes

Further results on robust H_∞ control design for uncertain time-delay systems with actuator delay: application to PMSG machine

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Delay-Independent Stability Conditions for Some Classes of Nonlinear Systems

Cited by 50 publications

References 26 publications

LMI-based robust tracking of a class of MIMO nonlinear systems

LMI-based robust tracking of a class of MIMO nonlinear systems

Stability Analysis of Ships’ Movement Along Optimal Routes

Further results on robust H∞ control design for uncertain time-delay systems with actuator delay: application to PMSG machine

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Product

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Further results on robust H_∞ control design for uncertain time-delay systems with actuator delay: application to PMSG machine