On improving the convergence rate of linear continuous‐time systems subject to asymmetrically constrained control

Baddou, Atmane; Naib, M.; Tadeo, Fernando; Benzaouia, Abdellah

doi:10.1155/mpe/2006/89429

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…For the bound γ 3 e −αt +γ 4 te −αt on (5.30) it has been shown in (Baddou et al, 2006) that the convergence rate is at least −α + , for an arbitrary > 0, i.e., the one stated in Theorem 5.5. For the bound γ 3 e −αt +γ 4 te −αt on (5.30) it has been shown in (Baddou et al, 2006) that the convergence rate is at least −α + , for an arbitrary > 0, i.e., the one stated in Theorem 5.5.…”

Section: Convergence Rate Of Cascaded Systemsmentioning

confidence: 99%

Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models

Babuška

Schutter

Lendek

et al. 2011

Studies in Fuzziness and Soft Computing

203

144

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VI PrefaceThe intended audience are graduate students and researchers both from academia and industry. For newcomers to the field, the book provides a concise introduction dynamic TS fuzzy models along with two methods to construct TS models for a given nonlinear system.While this monograph focusses mainly on the theory and methodology of state and parameter estimation in nonlinear distributed dynamic systems, the methods presented can readily be used in applications such as industrial processes, traffic systems, environmental systems, energy and water distribution networks, and so on.Supplementary information relevant to this book is available at the website:http://www.dcsc.tudelft.nl/fuzzybook/ Comments, suggestions, or questions concerning the book or the website are welcome. Interested readers are encouraged to get in touch with the authors using the contact information on the website.

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Section: Convergence Rate Of Cascaded Systemsmentioning

confidence: 99%

Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models

Babuška

Schutter

Lendek

et al. 2011

Studies in Fuzziness and Soft Computing

203

144

View full text Add to dashboard Cite

show abstract

“…In this work, the controller design methodology developed in [3] is applied to improve the convergence rate of linear continuous-time system with asymmetrical constrained control using a state observer. The obtained controller permits also to benefit from a large domain of admissible state and avoids discontinuities and saturations of the control vector.…”

Section: Discussionmentioning

confidence: 99%

“…Unfortunately, this estimation of a large set of initial states usually introduces discontinuities in the control vector. Some effort has been made to smooth these discontinuities (see [3], [15], [16], [23] and references therein). This paper proposes a methodology to smooth the control vector, when an observer is used to estimate the state.…”

Section: Index Terms-asymmetricmentioning

confidence: 99%

On Improving the Convergence Rate of Linear Continuous-Time Systems Under Constrained Control With State Observers

Baddou¹,

Tadeo

Benzaouia

2008

IEEE Trans. Circuits Syst. I

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A controller design methodology for linear continuous-time systems using a state observer is proposed. In particular, the objective is to smooth the discontinuity resulting from a piecewise linear control law previously proposed, which improves the convergence rate of systems under asymmetrically constrained control. The proposed method is based on the use of a non quadratic asymmetrical Lyapunov function. Both full-order observers and minimal order observers are considered to reconstruct the inaccessible state. The speed of convergence of the controlled system and the observer is improved, with smooth control vector components, that respect always the imposed asymmetric constraints.Index Terms-Asymmetric constrained control, convergence rate improvement, decay rate, linear systems, state observers.

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“…For the bound in (33), it has been shown that the convergence rate is α [32]. This means that the convergence rate of the system (32), and therefore, of the system (25) is determined by the convergence rate of the individual subsystems.…”

Section: A Cascaded Fuzzy Systemsmentioning

confidence: 99%

Stability of Cascaded Fuzzy Systems and Observers

Lendek

Babuška

Schutter³

2009

IEEE Trans. Fuzzy Syst.

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Abstract-A large class of nonlinear systems can be well approximated by Takagi-Sugeno (TS) fuzzy models with linear or affine consequents. It is well known that the stability of these consequent models does not ensure the stability of the overall fuzzy system. Therefore, several stability conditions have been developed for TS fuzzy systems. We study a special class of nonlinear dynamic systems that can be decomposed into cascaded subsystems, which are represented as TS fuzzy models. We analyze the stability of the overall TS system based on the stability of the subsystems and prove that the stability of the subsystems implies the stability of the overall system. The main benefit of this approach is that it relaxes the conditions imposed when the system is globally analyzed, thereby solving some of the feasibility problems. Another benefit is that by using this approach, the dimension of the associated linear matrix inequality (LMI) problem can be reduced. For naturally distributed applications, such as multiagent systems, the construction and tuning of a centralized observer may not be feasible. Therefore, we also extend the cascaded approach to the observer design and use fuzzy observers to individually estimate the states of these subsystems. A theoretical proof of stability and simulation examples are presented. The results show that the distributed observer achieves the same performance as the centralized one, while leading to increased modularity, reduced complexity, lower computational costs, and easier tuning. Applications of such cascaded systems include multiagent systems, distributed process control, and hierarchical large-scale systems.

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On improving the convergence rate of linear continuous‐time systems subject to asymmetrically constrained control

Cited by 5 publications

References 16 publications

Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models

Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models

On Improving the Convergence Rate of Linear Continuous-Time Systems Under Constrained Control With State Observers

Stability of Cascaded Fuzzy Systems and Observers

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