Non-linear observer design for one-sided Lipschitz systems: an linear matrix inequality approach

Zhang, W.; Su, Housheng; Liang, Yan; Han, Zhanghua

doi:10.1049/iet-cta.2011.0386

Cited by 112 publications

(93 citation statements)

References 24 publications

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“…The uncertainties ΔA, ΔB, ΔE, ΔC are said to be admissible if the formulae from (8) to (10) are satisfied, the structure of the uncertainties in (8)-(10) can be used to deal with robust control and estimation problems,(e.g., [9,[19][20][21][22][23]) references therein. Throughout this paper, we will make the following assumptions.…”

Section: T a A X T B B U T E E F X T D W Tmentioning

confidence: 99%

“…Due to Lebesgue measurability of uncertainty parameter perturbations, some full-order nonlinear state observers under consideration are of the form in [21][22][23][24]. It is noted that Assumption 4 does not lose any generality, a nonlinear observerbased state feedback controller for non-linear system (6)- (7) is stated by…”

Section: Stability Analysis Of the Error System For Nonlinear Observementioning

confidence: 99%

“…In many practice applications, the design of robust nonlinear observers is close to the actual dynamic behavior of nonlinear systems with uncertainty disturbance rather than linear observers. For examples, in a unified LMI framework, Zhang et al [21] discussed the non-linear observer design for one-sided Lipchitz non-linear systems by establishing sufficient conditions of the existence of the observer. Though the proposed approach was less conservative and simpler than some existing results in recent literature, the measured noise or disturbances in the nonlinear observer design was unfortunately not taken into account.…”

Section: Introductionmentioning

confidence: 99%

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2017

IRATJ

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This paper is concerned with stability analysis problem of nonlinear observer design for a class of multilink flexible manipulators (MLFMs). Specifically, the dynamics of the MLFM is modeled by the use of a Lagrangian approach. In a unified algebraic Riccati matrix equality (ARME) framework, one corresponding error-state system is proven to be asymptotic stable in the mean square (ASMS) for a nonlinear observer design with a known feedback gain; However, since feedback control input is dependent of systematic uncertainty, nonlinear observer design problem with an unknown feedback gain is investigated in the first place. Further, one expansion augment system is proven to remain ASMS in the nonlinear observer design. Therefore, sufficient and necessary conditions of the two desired nonlinear observers can be designed and derived from the developed theory. Finally, simulation studies are used to verify the electiveness of the proposed approach is illustrated by simulation studies.

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Section: T a A X T B B U T E E F X T D W Tmentioning

confidence: 99%

Section: Stability Analysis Of the Error System For Nonlinear Observementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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2017

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“…Define the state estimation error ( ) = ( ) −̂( ), and then it follows from (1)- (7) that [13][14][15][16][17] …”

Section: Design Of Gain Matrixmentioning

confidence: 99%

Robust Fault Detection for a Class of Uncertain Nonlinear Systems Based on Multiobjective Optimization

Yan

Wang

2015

Mathematical Problems in Engineering

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A robust fault detection scheme for a class of nonlinear systems with uncertainty is proposed. The proposed approach utilizes robust control theory and parameter optimization algorithm to design the gain matrix of fault tracking approximator (FTA) for fault detection. The gain matrix of FTA is designed to minimize the effects of system uncertainty on residual signals while maximizing the effects of system faults on residual signals. The design of the gain matrix of FTA takes into account the robustness of residual signals to system uncertainty and sensitivity of residual signals to system faults simultaneously, which leads to a multiobjective optimization problem. Then, the detectability of system faults is rigorously analyzed by investigating the threshold of residual signals. Finally, simulation results are provided to show the validity and applicability of the proposed approach.

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“…The systems under consideration include the classical Lipschitz nonlinear systems as special cases. Motivated by the methods proposed in Kheloufi et al 2 and Zhang et al, 18 we formulate the observer-based controller design issue for such systems into solving a set of LMIs, which are readily tractable via numerical software. Moreover, as the application of observer-based control design, we use the developed stabilization approach to a flexible link manipulator system.…”

Section: Introductionmentioning

confidence: 99%

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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Non-linear observer design for one-sided Lipschitz systems: an linear matrix inequality approach

Cited by 112 publications

References 24 publications

Untitled

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Robust Fault Detection for a Class of Uncertain Nonlinear Systems Based on Multiobjective Optimization

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

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