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Observer-based robust control of a (1 ≤ a <2) fractional-order uncertain systems: a linear matrix inequality approach

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IET CONTROL theory AND applications 2012年第2期6卷 229-234页

作者： Lan, Y. -H. Huang, H. -X. Zhou, Y. Xiangtan Univ Sch Informat Engn Xiangtan 411105 Hunan Peoples R China Xiangtan Univ Sch Math & Computat Sci Xiangtan 411105 Hunan Peoples R China

The study is concerned with a method of observer-based control for fractional-order uncertain linear systems with the fractional commensurate order a (1 <= a < 2) based on linear matrix inequality (LMI) approach. First, a sufficient condition for robust asymptotic stability of the observer-based fractional-order control systems is presented. Next, by using matrix's singular value decomposition and LMI techniques, the existence condition and method of designing a robust observer-based controller for such fractional-order control systems are derived. Unlike previous methods, the results are obtained in terms of LMIs, which can be easily obtained by Matlab's LMI toolbox. Finally, a numerical example demonstrates the validity of this approach.

关键词： robust asymptotic stability fractional commensurate order linear matrix inequality approach linear systems (1a<2) fractional order uncertain systems robust control Stability in control theory linear algebra (numerical analysis) singular value decomposition observers observer based robust control Matlab LMI toolbox Simulation, modelling and identification linear matrix inequalities uncertain systems asymptotic stability

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Improved delay-dependent stabilisation criteria for discrete systems with a new finite sum inequality

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IET CONTROL theory AND applications 2012年第3期6卷 448-453页

作者： Peng, C. Nanjing Normal Univ Sch Elect & Automat Engn Nanjing 210042 Jiangsu Peoples R China Shanghai Univ Sch Mechatron Engn & Automat Shanghai 200072 Peoples R China

This study introduces a new finite sum inequality to investigate the problem of delay-dependent stability analysis and controller synthesis for a discrete system with an interval time-varying input delay. By constructing a novel piecewise Lyapunov-Krasovskii functional and employing the proposed finite sum inequality to deal with sum items in the derivation of our results, simplified whereas improved delay-dependent stabilisation criteria are obtained with the less number of linear matrix inequalities scalar decision variables. numerical examples show the effectiveness of the proposed method.

关键词： controller synthesis delay-dependent stabilisation criteria discrete systems time-varying systems Lyapunov-Krasovskii functional Time-varying control systems stability control system synthesis Stability in control theory Control system analysis and synthesis methods interval time-varying input delay stability criteria finite sum inequality linear algebra (numerical analysis) delays Lyapunov methods linear matrix inequalities Discrete control systems linear matrix inequalities scalar decision variables Distributed parameter control systems delay-dependent stability analysis problem

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Adaptive observer design for the uncertain Takagi-Sugeno fuzzy system with output disturbance

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IET CONTROL theory AND applications 2012年第10期6卷 1351-1366页

作者： Dang, T. V. Wang, W. -J. Luoh, L. Sun, C. -H. Natl Cent Univ Dept Elect Engn Jhongli 32001 Taiwan Chung Hua Univ Dept Elect Engn Hsinchu 10608 Taiwan Tamkang Univ Dept Mech & Electromech Engn Tamsui 25137 Taipei County Taiwan

The study proposes an adaptive fuzzy observer for the uncertain Takagi-Sugeno (T-S) fuzzy system with output disturbance. First, an augmented fuzzy model is built by integrating the system state and the output disturbance together as new variables. Then, the desired adaptive fuzzy observer is designed to estimate the unavailable system state and the unknown output disturbance simultaneously. Based on Lyapunov theory and linear matrix inequalities (LMIs) tools, two main conditions are derived under which the fuzzy observer is designed. Finally, the procedure of the observer design is summarised and the effectiveness of the designed observer is demonstrated with a numerical example.

关键词： adaptive control output disturbance Stability in control theory control system synthesis Control system analysis and synthesis methods Fuzzy control LMI Lyapunov theory fuzzy systems uncertain Takagi-Sugeno fuzzy system Self-adjusting control systems Lyapunov methods linear algebra (numerical analysis) linear matrix inequalities augmented fuzzy model observers linear matrix inequalities tools system state Simulation, modelling and identification adaptive observer design T-S system

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Delay-dependent stability for fuzzy neutral system via state matrix decomposition

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IET CONTROL theory AND applications 2012年第11期6卷 1745-1751页

作者： Nian, X. Wang, X. Wang, Y. Sun, Z. Cent South Univ Sch Informat Sci & Engn Changsha 410075 Peoples R China

This study deals with the problem of delay-dependent stability for fuzzy neutral system. The matrix decomposition technique is used to deal with the cross terms. The main results are extended to the fuzzy neutral system with time-varying uncertainties. The stability criteria proposed in this study, which are expressed by linear matrix inequalities, are with simple form and have less slack variables. numerical examples are given to illustrate the effectiveness of the authors' methods.

关键词： state matrix decomposition technique neurocontrollers time-varying systems Time-varying control systems stability Stability in control theory Fuzzy control cross terms fuzzy systems stability criteria linear algebra (numerical analysis) delays delay-dependent stability fuzzy neutral system fuzzy control Neurocontrol linear matrix inequalities time-varying uncertainties matrix decomposition Distributed parameter control systems

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Improved resilient feedback stabilisation method for uncertain systems

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IET CONTROL theory AND applications 2012年第11期6卷 1654-1660页

作者： Mahmoud, M. S. Hussain, S. A. KFUPM Dept Syst Engn Dhahran 31261 Saudi Arabia

The problem of resilient stabilisation for a class of continuous-time uncertain systems having norm-bounded parametric uncertainties is investigated. Both static and dynamic output-feedback resilient controller design is considered. The goal is to robustly quadratically stabilise the uncertain plant considering the controller gain perturbations. Sufficient conditions for the existence of static output feedback and dynamic output feedback resilient controllers are derived in terms of linear matrix inequalities. A numerical example for each type of controllers is illustrated to demonstrate their effectiveness.

关键词： controller gain perturbations resilient feedback stabilisation method stability control system synthesis feedback continuous-time uncertain systems norm-bounded parametric uncertainties Stability in control theory Control system analysis and synthesis methods uncertain systems quadratic stability linear algebra (numerical analysis) dynamic output-feedback resilient controller design continuous time systems uncertain plant dynamic output feedback resilient controllers linear matrix inequalities static output feedback resilient controllers

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Results on reachable set estimation for linear systems with both discrete and distributed delays

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IET CONTROL theory AND applications 2012年第14期6卷 2346-2350页

作者： Zuo, Z. Fu, Y. Wang, Y. Tianjin Univ Sch Elect Engn & Automat Tianjin Key Lab Proc Measurement & Control Tianjin 300072 Peoples R China

This study reconsiders the problem of reachable set bounding for a class of linear systems in the presence of both discrete and distributed delays. Some new criteria are established where the useful term is retained when we estimate the upper bound of the derivative of the Lyapunov-Krasovskii functional. The free-weighting matrix technique is utilised to realise such a purpose. Moreover, the special structure constraint on the final expression of the derivative of the Lyapunov functional in the previous result of authors is removed. Consequently, a tighter bound of the reachable set is obtained. numerical examples are given to illustrate the merit of the proposed method comparing with the existing ones.

关键词： reachable set bounding linear systems linear systems class Discrete control systems distributed control estimation theory Stability in control theory algebra discrete delays reachable set estimation Lyapunov methods delays free-weighting matrix technique Lyapunov-Krasovskii functional derivative distributed delays Distributed parameter control systems discrete systems matrix algebra

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Observer-based robust stabilisation of a class of non-linear fractional-order uncertain systems: an linear matrix inequalitie approach

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IET CONTROL theory AND applications 2012年第18期6卷 2757-2764页

作者： Li, C. Wang, J. Lu, J. Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China Minist Educ China Key Lab Syst Control & Informat Proc Shanghai 200240 Peoples R China

This study focuses on the observer-based robust stabilisation problem of a class of non-linear fractional-order uncertain systems with admissible time-variant uncertainty and bounded perturbation on the observer gain. A sufficient condition for the robust asymptotic stability of the observer-based non-linear fractional-order uncertain systems is presented based on direct Lyapunov approach. Utilising the matrix's singular value decomposition method (SVD), the systematic robust stabilisation design algorithm is then proposed. All the results are obtained in terms of linear matrix inequalities. A numerical example is provided to illustrate the efficiency and advantage of the proposed algorithm.

关键词： direct Lyapunov approach perturbation techniques Stability in control theory control system synthesis Control system analysis and synthesis methods Nonlinear control systems observer gain observer-based robust stabilisation problem matrix robust asymptotic stability bounded perturbation singular value decomposition method linear algebra (numerical analysis) Lyapunov methods systematic robust stabilisation design algorithm nonlinear control systems uncertain systems admissible time-variant uncertainty linear matrix inequalities linear matrix inequalities approach singular value decomposition observers Simulation, modelling and identification asymptotic stability nonlinear fractional-order uncertain systems

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Exponential mean-square stabilisation for non-linear systems: sampled-data fuzzy control approach

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IET CONTROL theory AND applications 2012年第18期6卷 2765-2774页

作者： Koo, G. B. Park, J. B. Joo, Y. H. Yonsei Univ Dept Elect & Elect Engn Seoul 120749 South Korea Kunsan Natl Univ Dept Control & Robot Engn Kunsan 573701 Chonbuk South Korea

This study presents a sampled-data fuzzy control problem for non-linear systems with packet losses. A Takagi-Sugeno (T-S) fuzzy model is adopted for the non-linear systems and the packet loss is separately considered for the independent, identically distributed and Markovian cases. The sampled-data fuzzy controllers are designed for a T-S fuzzy model. Based on the closed-loop system, sufficient conditions are derived for the exponential mean-square stabilisation and formulated in terms of linear matrix inequalities. Finally, a numerical example is provided to verify the effectiveness of the proposed technique.

关键词： Takagi-Sugeno fuzzy model nonlinear systems closed-loop system stability packet losses Stability in control theory linear algebra (numerical analysis) exponential mean-square stabilisation sampled-data fuzzy controllers Fuzzy control sampled-data fuzzy control problem Nonlinear control systems T-S fuzzy model mean square error methods fuzzy control Interpolation and function approximation (numerical analysis) linear matrix inequalities

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Estimating the stability domain of spacecraft attitude with delayed feedback

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IET CONTROL theory AND applications 2012年第13期6卷 2076-2082页

作者： Zhu, Q. Hu, G. -D. Yin, Y. -X. Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China

This study deals with the estimation of the stability domain of the spacecraft attitude control system with delayed feedback. For autonomous functional-differential equations, by using the invariance principle, a general estimation theorem is established to explicitly estimate the stability domain. Furthermore, based on the estimation theorem and an applicable Lyapunov functional, an estimation criterion of the stability domain for the spacecraft attitude control system with delayed proportional-derivative (PD) controller is obtained. It is worth noting that the estimation criterion can be described as a generalised eigenvalue problem and thus can be solved by linear matrix inequality (LMI) optimisation techniques. Finally, numerical examples show the effectiveness of the estimation criterion.

关键词： Spatial variables control Optimisation techniques differential equations functional equations estimation criterion PD control general estimation theorem delayed proportional-derivative controller PD controller space vehicles autonomous functional-differential equation Aerospace control Lyapunov functional stability Nonlinear and functional equations (numerical analysis) Stability in control theory invariance principle linear matrix inequality spacecraft attitude control system Control system analysis and synthesis methods LMI optimisation technique Differential equations (numerical analysis) eigenvalues and eigenfunctions feedback linear algebra (numerical analysis) Lyapunov methods linear matrix inequalities delayed feedback optimisation stability domain estimation numerical example generalised eigenvalue problem Distributed parameter control systems Simulation, modelling and identification invariance parameter estimation delay systems attitude control

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Local stabilisation of uncertain linear time-invariant plant with bounded control inputs: parametric H_∞ loop-shaping approach

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IET CONTROL theory AND applications 2012年第11期6卷 1567-1576页

作者： Patra, S. Sen, S. Ray, G. Indian Inst Technol Dept Elect Engn Kharagpur 721302 W Bengal India

In this study, an attempt has been made to design an output feedback controller for local stabilisation of uncertain linear time-invariant plant with bounded control inputs. The design is accomplished via parametric H-infinity loop-shaping control by describing the uncertainty as perturbations to normalised coprime factors of the shaped plant. The shaped plant is designed based on the closed-loop design specifications by appropriately choosing the weighting transfer function matrices. For the existence of stabilising controller, a set of sufficient conditions has been derived in linear matrix inequality framework and subsequently, a region of attraction is estimated such that the control inputs never exceed the pre-specified bounds. To illustrate the effectiveness of the proposed method, a numerical example has been elucidated.

关键词： H∞ control shaped plant bounded control inputs local stabilisation linear matrix inequality framework normalised coprime factors stability control system synthesis Stability in control theory Control system analysis and synthesis methods stabilising controller weighting transfer function matrices linear systems output feedback controller design uncertain linear time-invariant plant feedback linear algebra (numerical analysis) parametric H∞ loop-shaping approach uncertain systems linear matrix inequalities Optimal control transfer function matrices

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