Stabilisation for a class of non-linear uncertain systems based on interval observers

Cai, Xiushan; Lv, Guorong; Zhang, W.

doi:10.1049/iet-cta.2011.0493

Cited by 25 publications

(14 citation statements)

References 11 publications

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“…The objective of this work is to design an interval observer for the system (4). Note that, in a related work [29], an interval observer for such a class of systems has been proposed in the context of systems stabilization (see also the first work on application of interval observers for stabilization of LPV systems [30], another version is given in [31]), where the stability of the interval observer was ensured by a proper choice of control input dependent on the observer state. In other words, in [29] stability of the interval estimation error dynamics is not established in the observer design step.…”

Section: A Problem Statementmentioning

confidence: 99%

Interval observers for continuous-time LPV systems with L1/L2 performance

et al. 2015

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An approach to interval observer design for Linear Parameter-Varying (LPV) systems is proposed. It is assumed that the vector of scheduling parameters in LPV models is not available for measurement. Two different interval observers are constructed for nonnegative systems and for a generic case. Stability conditions are expressed in terms of matrix inequalities, which can be solved with respect to the observer gains using standard numerical solvers. Applying L1/L2 framework the robustness and estimation accuracy with respect to model uncertainty are analyzed. The efficiency of interval estimation for LPV models is demonstrated through numerical experiments for a microfluidic system and an academic example. I. INTRODUCTIONState estimation is an important issue in many engineering fields [1], [2], [3]. Estimated states may be required, for example, for control design or fault detection. This problem has been widely studied in the literature and many solutions already exist for linear systems and a number of nonlinear structures. For the latter situation, the observer design problem is solvable if the system model can be transformed into a canonical form, which may be a hard assumption to satisfy in many applications. To solve the problem, an appealing approach is based on the LPV transformation of the nonlinear system [4], [5], [6], [7].Note that Takagi-Sugeno decomposition can be another alternative solution to deal with nonlinear systems and to obtain the equivalent representation by a compact set of linear state space models with nonlinear weighting functions satisfying the convex sum property [8], [9]. In the presence of uncertainty (unknown parameters or/and external disturbances) the design of a conventional estimator, converging to the ideal value of the state, cannot be realized. However, an interval estimation may still remain feasible: an observer can be constructed that, using input-output information, evaluates the set of admissible values (interval) for the state at each instant of time. The interval length has to be minimized and it is proportional to the size of the model uncertainty. Despite such a formulation looks like a simplification of the state estimation problem, in fact it is an improvement since the interval mean can be used as the state pointwise estimate, while the interval limits give the admissible deviations from that value (thus, an interval estimator provides a simultaneous accuracy evaluation for bounded uncertainty, which may not have a known statistics). There are several approaches to design interval/set-membership estimators [10], [11], [12], [13]. This paper continues the trend of interval observer design based on the monotone systems theory [12], [13], [14], [15], [16]. In such a way the main restriction for the interval observer design consists in providing cooperativity of the interval estimation error dynamics by a proper design. Such a complexity has been recently overcame in [17], [15], [18] for LTI systems. In those studies, it has beenshown that under some mild condition...

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Section: A Problem Statementmentioning

confidence: 99%

Interval observers for continuous-time LPV systems with L1/L2 performance

et al. 2015

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“…The design of a controller for dynamical systems using the extracted boundaries caused by interval observer has been focused on some studies on parameter‐varying [20], non‐linear [21, 22], switching [23], descriptor [24], impulsive [25], and large‐scale [26] systems. Nevertheless, many unsolved issues on interval OBC (IOBC) methods have been remained due to the problems, such as large number of state variables, controllability, and tracking problems that led to the increase in the number of studies.…”

Section: Introductionmentioning

confidence: 99%

Robust integral feedback control based on interval observer for stabilising parameter‐varying systems

Faramin¹,

Rezaie

Rafiee

2019

IET Control Theory & Applications

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“…Some of these properties, for example, the state trajectories of positive systems being determined by the initial conditions and forcing input, can be used to analyse error dynamics systems in the study of a state estimation. In particular, the discussion of state estimation can be traced back to the seminal work by Schweppe [5]; however, the methodology for a state estimation based on an interval observer is more recent [6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Control of non‐linear systems based on interval observer design

Xie

2018

IET Control Theory & Applications

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Stabilisation for a class of non-linear uncertain systems based on interval observers

Cited by 25 publications

References 11 publications

Interval observers for continuous-time LPV systems with L1/L2 performance

Interval observers for continuous-time LPV systems with L1/L2 performance

Robust integral feedback control based on interval observer for stabilising parameter‐varying systems

Control of non‐linear systems based on interval observer design

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