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On multiobjective synthesis for parameter-dependent descriptor systems

IET CONTROL theory AND applications 2010年第5期4卷 817-826页

作者： Yagoubi, M. IRCCyN CNRS UMR 6597 Nantes 3 France EMN F-44307 Nantes France

This note proposes dilated (or extended) linear matrix inequality (LMI) characterisations of admissibility, D-admissibility, H-infinity and H-2 norms for continuous-time descriptor systems. As for state-space systems, these LMIs achieve less conservative results when dealing with robust admissibility/performance analysis of affine parameter-dependent descriptor systems. Furthermore, an iterative design procedure for multiobjective state-feedback control of parameter-dependent descriptor systems is presented based on these dilated LMI conditions. The main idea underlying the proposed method is to linearise the products of controller parameter and the auxiliary variable by assigning the last one. In the initialisation step of the proposed algorithm, the assignment takes into account an explicit characterisation of the auxiliary variable. The effectiveness of the proposed conditions and design method is shown through some numerical examples.

关键词： multiobjective state feedback control multiobjective synthesis H infinity linear matrix inequality characterisations D-admissibility linear algebra (numerical analysis) Control system analysis and synthesis methods affine parameter-dependent descriptor systems continuous time descriptor systems iterative design procedure state feedback state-space methods performance analysis continuous time systems linear matrix inequalities state-space systems robust admissibility

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Improved stability criteria for linear systems with time-varying delay

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IET CONTROL theory AND applications 2010年第4期4卷 683-689页

作者： Sun, J. Liu, G. P. Chen, J. Rees, D. Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China Univ Glamorgan Fac Adv Technol Pontypridd CF37 1DL M Glam Wales Harbin Inst Technol CTGT Ctr Harbin 150001 Peoples R China

This study is concerned with the stability analysis of systems with time-varying delay in a given interval. A new type of augmented Lyapunov functional which contains some triple-integral terms is proposed. By introducing free-weighting matrices, a new delay-range-dependent stability criterion is derived in terms of linear matrix inequality. The rate-range of the delay is considered, so the stability criterion is also delay-rate-range dependent. numerical examples are given to illustrate the effectiveness of the proposed method.

关键词： free-weighting matrices stability criteria linear systems control system analysis Lyapunov functional Stability in control theory algebra delays Lyapunov methods linear matrix inequality stability analysis Control system analysis and synthesis methods delay-range-dependent stability criterion Distributed parameter control systems time-varying delay linear matrix inequalities triple-integral terms

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Modelling and stabilisation of networked control system with packet loss and time-varying delays

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IET CONTROL theory AND applications 2010年第6期4卷 1094-1100页

作者： Ye, X. Liu, S. Liu, P. X. Harbin Engn Univ Coll Automat Harbin 150001 Peoples R China Carleton Univ Dept Syst & Comp Engn Ottawa ON K1S 5B6 Canada

The modelling and stabilising control of networked control systems (NCSs) with stochastic packet loss and time-varying delays are addressed. In specific, a novel Markovian jump linear system with time-varying delays is used to model the NCS. Without using the augmented state method, sufficient conditions for the stochastic stabilisation of the NCS with packet loss and time-varying delays are obtained via the mode-dependent Lyapunov function method. The mode-dependent controller for the closed-loop NCS is presented in the linear matrix inequalities formulation via the Shur complement theory. A numerical example is given to illustrate the effectiveness of the proposed method.

关键词： linear matrix inequalities formulation stochastic packet loss mode-dependent controller packet loss closed-loop NCS stabilising control Markovian jump linear system Lyapunov function method time-varying systems Time-varying control systems stability Stability in control theory closed loop systems algebra Lyapunov methods delays networked control system linear matrix inequalities Markov processes time-varying delays Shur complement theory Distributed parameter control systems

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H_∞ model reduction of linear continuous-time systems over finite-frequency interval

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IET CONTROL theory AND applications 2010年第3期4卷 499-508页

作者： Du, X. Yang, G. -H. Northeastern Univ Coll Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Northeastern Univ Minist Educ Key Lab Integrated Automat Proc Ind Shenyang 110004 Liaoning Peoples R China

This article studies the H-infinity model reduction problem for linear continuous-time systems over a finite-frequency interval. Different from the existing methods in the literature, we resort to the aid of recently developed generalised Kalman-Yakubovich-Popov (GKYP) lemma. Based on a in-depth exploitation of the GKYP lemma and the Projection lemma, sufficient conditions for the finite-frequency H-infinity model reduction problems are derived and expressed in terms of solutions to a set of linear matrix inequalities (LMIs), which can be handled easily by using the available toolbox. numerical examples are included for illustration.

关键词： H∞ control reduced order systems linear systems projection lemma algebra generalised Kalman-Yakubovich-Popov lemma Optimal control Control system analysis and synthesis methods sufficient conditions linear continuous-time systems continuous time systems H∞ model reduction linear matrix inequalities finite-frequency interval

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Delay-dependent robust H_∞ control of time-delay systems

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IET CONTROL theory AND applications 2010年第7期4卷 1122-1130页

作者： Sun, M. Jia, Y. NE Univ Qinhuangdao Dept Automat & Engn Qinhuangdao 066004 Hebei Peoples R China Beihang Univ Dept Syst & Control Beijing 100083 Peoples R China

In this study, a delay-dependent H-infinity performance criterion that possess decoupling structure is derived for a class of time-delay systems. It is then extended to H-infinity state-feedback synthesis for time-delay systems with polytopic uncertainty and multichannel H-infinity dynamic output-feedback synthesis for time-delay systems. All the conditions are given in terms of the linear matrix inequalities. In some previous descriptor methods, the products of controller matrices and Lyapunov matrices are completely separated in performance analysis, whereas it is not the case in controller synthesis. However, with the method in the paper, the weakness is eliminated. numerical examples illustrate the effectiveness of our solutions as compared to results obtained by other methods.

关键词： H∞ control delay-dependent H∞ performance criterion time-delay systems Stability in control theory control system synthesis Control system analysis and synthesis methods state feedback Lyapunov matrix equations H∞ state-feedback synthesis robust control decoupling structure multichannel H∞ dynamic output-feedback synthesis linear algebra (numerical analysis) controller matrices uncertain systems linear matrix inequalities Lyapunov matrices Optimal control delay-dependent robust H∞ control polytopic uncertainty Distributed parameter control systems delay systems

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Computing estimates of the region of attraction for rational control systems with saturating actuators

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IET CONTROL theory AND applications 2010年第3期4卷 315-325页

作者： Coutinho, D. F. Gomes da Silva, J. M., Jr. PUCRS GACS BR-90619900 Porto Alegre RS Brazil Univ Fed Rio Grande do Sul Dept Elect Engn BR-90035190 Porto Alegre RS Brazil

This study focuses on the problem of regional stability analysis of rational control systems with saturating actuators. Estimates of the region of attraction are computed by means of invariant domains associated to rational Lyapunov functions. Conditions for computing these invariant domains (regions of stability) are proposed in the form of linear matrix inequalities (LMIs). These conditions are derived considering a differential-algebraic representation of the rational system dynamics. The saturation effects are taken into account by means of a generalised sector condition for deadzone non-linearities. The obtained conditions are cast in convex optimisation schemes in order to compute a Lyapunov function which leads to a maximised estimate of the region of attraction.

关键词： deadzone nonlinearities Optimisation techniques convex programming rational Lyapunov functions differential algebraic equations stability Stability in control theory rational control systems Actuating and final control devices LMI Nonlinear control systems regional stability analysis Differential equations (numerical analysis) linear algebra (numerical analysis) Lyapunov methods saturating actuators nonlinear control systems rational system dynamics linear matrix inequalities generalised sector condition convex optimisation schemes nonlinear control systems theory actuators differential-algebraic representation

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Stability analysis of interconnected time-delay systems in a generalised framework

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IET CONTROL theory AND applications 2010年第12期4卷 3022-3032页

作者： Ghosh, S. Das, S. K. Ray, G. Natl Inst Technol Dept Elect Engn Rourkela 769008 India Indian Inst Technol Dept Elect Engn Kharagpur 721302 W Bengal India

Stability analysis of interconnected systems with finite as well as arbitrary interconnection delays is considered in this study. For the purpose, subsystems interconnected with finite delays are grouped to form larger subsystems with intraconnection delays. However, these larger subsystems are interconnected with arbitrary delays among themselves. By considering a suitable Lyapunov-Krasovskii functional, a stability criterion is derived in the linear matrix inequality (LMI) framework to study simultaneous delay-independent (for the interconnection delays) and delay-dependent (for the intraconnection delays) stability of the reformed interconnected system. This proposed criterion is useful when one attempts to estimate the tolerable bounds of the intraconnection delays. Finally, a numerical example is considered to illustrate the effectiveness of the proposed criterion.

关键词： interconnected systems delay independent stability interconnected time delay system stability algebra Stability in control theory delays Lyapunov methods stability analysis linear matrix inequality finite delay interconnected subsystem Multivariable control systems Distributed parameter control systems linear matrix inequalities time-varying systems

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Co-design of predictive controllers for wireless network control

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IET CONTROL theory AND applications 2010年第2期4卷 186-196页

作者： Irwin, G. W. Chen, J. McKernan, A. Scanlon, W. G. Queens Univ Belfast Sch Elect Elect Engn & Comp Sci Belfast Antrim North Ireland

This study presents a co-design approach to wireless network control systems (WNCS). Experimental studies are carried out to identify and analyse the delays inherent in WNCS, with a new inverse Gaussian model for their statistical distribution proposed. Two different packet-based predictive control schemes are presented. One uses dynamic matrix control (DMC), the other is a linear quadratic (LQ) controller incorporating multiple observers. Lyapunov stability is derived using linear matrix inequalities (LMIs) for the multi-observer LQ control whereas Monte-Carlo simulation results on a cart-mounted inverted pendulum are presented to confirm the performance advantages of packet-based DMC. Finally, results from a real-time implementation of the multi-observer LQ controller are also presented.

关键词： statistical distributions statistical distribution Lyapunov stability predictive control wireless network control system codesign control system analysis linear quadratic controller stability Stability in control theory linear quadratic control Control system analysis and synthesis methods Gaussian processes inverse Gaussian model dynamic matrix control predictive controller distributed control delay linear algebra (numerical analysis) delays Optimal control linear matrix inequalities Monte-Carlo simulation Monte Carlo methods multi-observer LQ control cart mounted inverted pendulum Distributed parameter control systems

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Decentralised state feedback design for large-scale linear systems subject to input saturation

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IET CONTROL theory AND applications 2010年第2期4卷 206-227页

作者： Lu, L. Lin, Z. Bateman, A. Shanghai Jiao Tong Univ Dept Automat Shanghai 200030 Peoples R China Univ Virginia Charles L Brown Dept Elect & Comp Engn Charlottesville VA 22904 USA

This study considers the design of decentralised controllers for large-scale linear systems under actuator saturation. Saturation in the magnitude of the control input is first considered. For the closed-loop system under a saturating decentralised state feedback law, conditions are identified under which an ellipsoid is contractively invariant and thus within the domain of attraction, or the restricted L-2 gain from the disturbance to the output is less than or equal to a pre-specified value gamma. Based on these conditions, the designs of decentralised state feedback laws that achieve large domains of attraction or low L-2 gains can be formulated as optimisation problems with bilinear matrix inequality (BMI) constraints. numerical algorithms are developed to solve these BMI problems. These developments are also extended to the situation where the inputs are subject to nested saturation, such as simultaneous actuator magnitude and rate saturation. Throughout the study, numerical examples are used to demonstrate the effectiveness of the proposed design method.

关键词： decentralised controllers control nonlinearities large-scale linear systems Multivariable control systems control system synthesis input saturation actuator saturation Control system analysis and synthesis methods Nonlinear control systems decentralised state feedback design state feedback closed loop systems linear systems large-scale systems linear algebra (numerical analysis) decentralised control linear matrix inequalities closed-loop system bilinear matrix inequality constraints

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H_∞ static output feedback control for discrete-time switched linear systems with average dwell time

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IET CONTROL theory AND applications 2010年第3期4卷 381-390页

作者： Ding, D. -W. Yang, G. -H. Northeastern Univ Coll Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Northeastern Univ Minist Educ Key Lab Integrated Automat Proc Ind Shenyang 110004 Liaoning Peoples R China

This study investigates the problem of H-infinity static output feedback (SOF) control for discrete-time switched linear systems with average dwell time. By the aid of multiple Lyapunov functions combined with Finsler's lemma, a switched SOF controller is designed such that the closed-loop switched system is exponentially stable and achieves a weighted L-2-gain. Sufficient conditions for SOF control are derived and formulated in terms of linear matrix inequalities (LMIs). The minimal average dwell time and the corresponding SOF controller are obtained from the LMI conditions for a given system decay degree. The proposed method is less conservative than the existing ones, which is validated by a numerical example.

关键词： H∞ control linear systems Lyapunov functions Discrete control systems Stability in control theory feedback algebra H∞ static output feedback control Lyapunov methods LMI linear matrix inequalities average dwell time discrete time switched linear systems discrete time systems Optimal control SOF closed-loop switched system

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