Robust Observer and Observer‐Based Controller for Time‐Delay Singular Systems

Hassan, Lama; Zemouche, Ali; Boutayeb, Mohamed

doi:10.1002/asjc.669

Cited by 14 publications

(13 citation statements)

References 30 publications

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“…Let P be an (unknown) positive definite symmetric matrix. Define the function V 1 as in (9). Then for its derivative holdṡ…”

Section: Observer Designmentioning

confidence: 99%

“…where V 1 , V 2 , V 3 are defined by (9,10,11). Let P be an (unknown) positive definite symmetric matrix.…”

Section: Observer Designmentioning

confidence: 99%

“…However, there have been some results available for relatively short period. Robust observer constructed using linear matrix inequalities is presented in [1] and [9]. Linear observer is proposed by [10].…”

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confidence: 99%

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Sum-of-squares observer design for a polynomial system with unknown time delays

Rehák

2014

11th IEEE International Conference on Control &Amp; Automation (ICCA)

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The topic of the paper is a procedure for observer design for polynomial systems. The design is based on sum-ofsquares through construction of suitable Lyapunov-Krasovskii functionals. As the resulting problem is not convex, an iterative formula is proposed to obtain the solution. Estimates of observation error are derived, the usage of the method is illustrated by an example. I. INTRODUCTIONOne of most important problems in the control theory is the design of observer. Concerning nonlinear ones, high gain observers (for more details, [13] and references therein) have gained big importance. Unfortunately, their behavior is somewhat compromised by high sensitivity to noise.In practical control theory, time delay systems are encountered very often. There is small wonder that there is a strong call for reliable and efficient control algorithms for these systems. In the control design for plants exhibiting this kind of behavior, Lyapunov-Krasovskii functionals play an important role, see [8] and references therein. One can convert the controller design problem for time-delay systems into the problem of finding a set of solutions of linear matrix inequalities (LMI) which can be efficiently solved. For example, let us mention [18], [14], [23] where an iterative algorithm is proposed. In each iteration, a LMI is solved. Nonlinearities might be treated using the robust control approach. The time delay might be unknown or changing. Design of observer for time-delay systems is proposed in [17]. Here, nonlinearities have to be treated by robust control as well. Works dealing with quantization ([5]) are also available. They also use similar LyapunovKrasovskii functionals. Singular systems are treated in [31] using a similar methodology, the functionals being only slightly modified.So far, the observer design for time-delay systems is a field that is not fully explored. However, there have been some results available for relatively short period. Robust observer constructed using linear matrix inequalities is presented in [1] and [9]. Linear observer is proposed by [10]. Nonlinear systems with Lipschitz nonlinearity are treated in [3]. Here, the design relies on design of a suitable Lyapunov-Krasovskii functional leading to the problem of finding a solution of a certain LMI.[19] uses a neural network-based approach to design an observer.

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“…Let P be an (unknown) positive definite symmetric matrix. Define the function V 1 as in (9). Then for its derivative holdṡ…”

Section: Observer Designmentioning

confidence: 99%

“…where V 1 , V 2 , V 3 are defined by (9,10,11). Let P be an (unknown) positive definite symmetric matrix.…”

Section: Observer Designmentioning

confidence: 99%

See 1 more Smart Citation

Sum-of-squares observer design for a polynomial system with unknown time delays

Rehák

2014

11th IEEE International Conference on Control &Amp; Automation (ICCA)

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“…As not all system states can be measured, an observer based output feedback control will be employed. A number of candidate asymptotic observers have been presented for second order nonlinear systems using a range of design paradigms including a high gain nonlinear state observer [11], a sliding mode observer [12], an adaptive nonlinear observer [13] and a robust observer designed using Lyapunov techniques and using LMIs [14]. By combining such observers with existing state feedback control methodologies, various output feedback control strategies have been designed [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Adaptive output feedback finite time control for a class of second order nonlinear systems

Zhao

Spurgeon

Yan

2016

2016 14th International Workshop on Variable Structure Systems (VSS)

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Abstract-This paper develops a finite time output feedback based control scheme for a class of nonlinear second order systems. The system representation includes both model uncertainty and uncertain parameters. A finite time parameter estimator is developed. This facilitates the design of a finite time observer based on the well-established step-by-step sliding mode observer design approach. A terminal sliding mode control scheme is then developed using the corresponding state estimates. The methodology is applied to a continuous stirred tank reactor system to validate the effectiveness of the proposed approach.

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“…That is why observer-based control problems and observer design problems, which are involved with using the available information on inputs and outputs to reconstruct the unmeasured states of the concerned system, have been wide investigated in many practical applications (20)(21)(22) . However, only a few works have been carried out on singular systems (23,24) , not to mention on the ones simultaneously considering…”

Section: Introductionmentioning

confidence: 99%

An Observer-Based Controller Design for a Markovian Jumping Singular System with Polytopic Uncertainties

Lee

Huang

Kung

2017

The Proceedings of the 5th International Conference on Industrial Application Engineering 2017

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In this paper, an observer-based controller design problem for a discrete-time Markovian jumping singular system (DMJSS) with polytopic uncertainties is considered, which is based on a set of necessary and sufficient conditions in terms of linear matrix inequalities (LMIs) for an admissibility analysis problem. A proposed mode dependent observer and a controller can be designed separately via two sets of derived LMI-based synthesis conditions. There are two principal contributions in this paper. One is that a set of strictly LMI-based necessary and sufficient conditions for the admissibility analysis problem for a DMJSS is extended to the case with uncertainties. Another one is that a suitable observer and a controller can be designed independently via two sets of strictly LMI-based synthesis conditions instead of a set of complex algorithm in terms of bilinear or nonconvex inequalities.

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Robust Observer and Observer‐Based Controller for Time‐Delay Singular Systems

Cited by 14 publications

References 30 publications

Sum-of-squares observer design for a polynomial system with unknown time delays

Sum-of-squares observer design for a polynomial system with unknown time delays

Adaptive output feedback finite time control for a class of second order nonlinear systems

An Observer-Based Controller Design for a Markovian Jumping Singular System with Polytopic Uncertainties

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