Nonlinear observer design for one-sided Lipschitz systems

Abbaszadeh, Masoud; Marquez, Horacio J.

doi:10.1109/acc.2010.5530715

Cited by 220 publications

(315 citation statements)

References 13 publications

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“…The quadratic innerboundedness condition 17 is also introduced, which is very helpful for obtaining LMI-type synthesis conditions. Definition 1.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…Additionally, the one-sided Lipschitz constants can be chosen much smaller than the Lipschitz constants. [13][14][15][16][17] Moreover, if a function is Lipschitz, it is both one-sided Lipschitz and quadratically inner-bounded; however, the converse is not ture. 17 Therefore, the nonlinear plant considered in our work encompasses the Lipschitz nonlinear system as a special case (see Figure 1).…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…[13][14][15][16] It is shown that the one-sided Lipschitz encompasses a large class of nonlinearities and can reduce conservatism in the existing designs. Abbaszadeh and Marquez 17 further studied the state estimation problem of one-sided Lipschitz systems by introducing an additional restrict called quadratically inner-bounded condition. For such systems, less conservative designs on both full-order and reduced-order observers have been considered by Zhang et al 18,19 where the Riccati equation and the LMI approaches were, respectively, introduced.…”

Section: Introductionmentioning

confidence: 99%

“…13 In our study, we assume that the system nonlinear function satisfies the standard one-sided Lipschitz condition and is quadratically innerbounded. 17 On the other hand, to design the observerbased controller, the challenge is to analyze the Lyapunov stability of closed-loop systems. 9 Generally, one needs to solve a kind of bilinear matrix inequalities (BMIs).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Observer-based stabilization of one-sided Lipschitz systems with application to flexible link manipulator

Zhang

Song

et al. 2015

Advances in Mechanical Engineering

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This article is concerned with the observer-based output feedback stabilization problem for a class of nonlinear systems that satisfies the one-sided Lipschitz and the quadratically inner-bounded conditions. The system model under consideration encompasses the classical Lipschitz nonlinear system as a special case. For such a system, we design the output feedback controller via constructing a full-order Luenberger-type state observer. Sufficient conditions that guarantee the existence of observer-based output feedback are established in the form of linear matrix inequalities, which are readily solved by the available numerical software. Moreover, the proposed observer-based output feedback designs are applied to a flexible link manipulator system. Finally, simulation study on the manipulator system is given to demonstrate the effectiveness of the developed control design.

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“…The quadratic innerboundedness condition 17 is also introduced, which is very helpful for obtaining LMI-type synthesis conditions. Definition 1.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Observer-based stabilization of one-sided Lipschitz systems with application to flexible link manipulator

Zhang

Song

et al. 2015

Advances in Mechanical Engineering

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show abstract

“…In this paper, we consider the class of discrete-time nonlinear systems described by Figure 1 The Lipschitz, one-sided Lipschitz, and quadratically inner-bounded function sets [24].…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

State estimation for discrete-time systems with generalized Lipschitz nonlinear dynamics

Wang¹,

Song²,

Zhang³

2015

Adv Differ Equ

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This paper considers the state estimation problem for a class of discrete-time systems with generalized Lipschitz nonlinear dynamics. Under the assumption that the system nonlinearities satisfy a quadratically inner-boundedness condition, we design both the full-order observer and the reduced-order observer for the discrete-time nonlinear system. Sufficient conditions ensuring the existence of full-order observers as well as reduced-order observers for such systems are established and formulated in terms of linear matrix inequality (LMI). Compared with some existing results, we remove the one-sided Lipschitz restrict and extend the classical Lipschitz observer design to a larger class of discrete-time nonlinear systems. A numerical example is included to illustrate the effectiveness of the proposed design.

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Security‐based fault detection filtering design for fuzzy singular semi‐Markovian jump systems via improved dynamic event‐triggering and quantization protocols

Kong,

Luo,

Cheng

et al. 2023

Adaptive Control & Signal

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SummaryThis article concerns the problem of event‐protocol‐based asynchronous fault detection filtering design for discrete‐time fuzzy singular semi‐Markovian jump systems subjected to system parameters uncertainties, unmatched one‐sided Lipschitz nonlinearities and multi‐cyber‐attacks. First, a well‐designed model structure is proposed to integrate two dynamic quantizers and an improved dynamic event‐triggered protocol into a unified framework to reduce the amount of data in the network transmission and rationalize the use of limited network communication bandwidth resources. Especially, the event‐triggering threshold parameter can be continuously adjusted over the time based on the fluctuation of the network signal. Second, a novel triple‐cyber‐attacks platform is established, of which including random deception attacks, random replay attacks and aperiodic DoS attacks. And with help of the extended decoupling strategy and iterative techniques, the co‐design conditions of the stochastic admissibility with a level of performance are derived for the fault filtering error systems. Finally, two examples are provided to demonstrate the effectiveness and feasibility of the proposed algorithm.

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Nonlinear observer design for one-sided Lipschitz systems

Cited by 220 publications

References 13 publications

Observer-based stabilization of one-sided Lipschitz systems with application to flexible link manipulator

Observer-based stabilization of one-sided Lipschitz systems with application to flexible link manipulator

State estimation for discrete-time systems with generalized Lipschitz nonlinear dynamics

Security‐based fault detection filtering design for fuzzy singular semi‐Markovian jump systems via improved dynamic event‐triggering and quantization protocols

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