Stability and stabilization of continuous descriptor systems: An LMI approach

This paper deals with the problems of robust stability and stabilization for uncertain continuous descriptor systems. We propose a new necessary and sufficient condition in terms of a strict linear matrix inequality (LMI) for a nominal continuous descriptor system to be admissible (stable, regular, and impulse-free). Based on this, the state-feedback admissibility problem is solved and the solution is extended to the case of uncertain descriptor systems. Finally, numerical examples are given to illustrate the results.

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Robust Stability and Stabilization of Interval Uncertain Descriptor Fractional-Order Systems with the Fractional-Orderα: The1≤α<2Case

Mathematical Problems in Engineering ◽

10.1155/2015/606048 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Yuanhua Li ◽

Heng Liu ◽

Hongxing Wang

Keyword(s):

Fractional Order ◽

Sufficient Conditions ◽

Linear Matrix ◽

Fractional Order Systems ◽

Matrix Inequalities ◽

Interval System ◽

Interval Coefficients ◽

Stability And Stabilization ◽

Necessary And Sufficient ◽

Robust Stability And Stabilization

Stability and stabilization of fractional-order interval system is investigated. By adding parameters to linear matrix inequalities, necessary and sufficient conditions for stability and stabilization of the system are obtained. The results on stability check for uncertain FO-LTI systems with interval coefficients of dimensionnonly need to solve one 4n-by-4nLMI. Numerical examples are presented to shown the effectiveness of our results.

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Observers of Fuzzy Descriptor Systems with Time-Delays

Abstract and Applied Analysis ◽

10.1155/2014/714518 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Hongbiao Fan ◽

Min Meng ◽

Jun-e Feng

Keyword(s):

Time Delays ◽

Discrete Systems ◽

Descriptor Systems ◽

Linear Matrix ◽

Equivalent Transformation ◽

Matrix Inequality ◽

Lmi Approach ◽

State Observers ◽

Delay Dependent ◽

Fuzzy State

For discrete fuzzy descriptor systems with time-delays, the problem of designing fuzzy observers is investigated in this paper. Based on an equivalent transformation, discrete fuzzy descriptor systems with time-delays are converted into standard discrete systems with time-delays. Then, via linear matrix inequality (LMI) approach, both delay-dependent and delay-independent conditions for the existence of fuzzy state observers are obtained. Finally, two numerical examples are provided to illustrate the proposed method.

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SpecificD-Admissibility and Design Issues for Uncertain Descriptor Systems with Parametric Uncertainty in the Derivative Matrix

Mathematical Problems in Engineering ◽

10.1155/2016/6142848 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12

Author(s):

Chih-Peng Huang

Keyword(s):

Controller Design ◽

State Space Model ◽

Parametric Uncertainty ◽

Descriptor Systems ◽

Descriptor System ◽

Linear Matrix ◽

Closed Loop Systems ◽

Derivative Matrix ◽

Feasible Solutions ◽

Necessary And Sufficient

Stability analysis issues and controller synthesis for descriptor systems with parametric uncertainty in the derivative matrix are discussed in this paper. The proposed descriptor system can extend the system’s modeling extent of physical and engineering systems from the traditional state-space model. First, based on the extendedD-stability definitions for the descriptor model, necessary and sufficient admissibility andD-admissibility conditions for the unforced nominal descriptor system are derived and formulated by compact forms with strict linear matrix inequality (LMI) manner. In contrast, existing results need to involve nonstrict LMIs, which cannot be evaluated by current LMI solvers and need some extra treatments. Deducing from the obtained distinct results, the roust admissibility andD-admissibility of the descriptor system with uncertainties in both the derivative matrix and the system’s matrices thus can be coped. Furthermore, by involving a proportional and derivative state feedback (PDSF) control law, we further address the controller design for the resulting closed-loop systems. Since all the proposed criteria are explicitly expressed in terms of the strict LMIs, we can use applicable LMI solvers for evaluating the feasible solutions. Finally, the efficiency and practicability of the proposed approach are demonstrated by two illustrative examples.

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Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach

IEEE Transactions on Automatic Control ◽

10.1109/9.618244 ◽

1997 ◽

Vol 42 (8) ◽

pp. 1144-1148 ◽

Cited By ~ 367

Author(s):

Xi Li ◽

C.E. de Souza

Keyword(s):

Linear Matrix Inequality ◽

Robust Stability ◽

Delay Systems ◽

Linear Matrix ◽

Matrix Inequality ◽

Linear Delay ◽

Linear Matrix Inequality Approach ◽

Stability And Stabilization ◽

Delay Dependent ◽

Robust Stability And Stabilization

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Hinf Control of Uncertain Takagi-Sugeno Fuzzy Descriptor Systems

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.694-697.2110 ◽

2013 ◽

Vol 694-697 ◽

pp. 2110-2115

Author(s):

Bao Ping Ma ◽

Ming Chen

Keyword(s):

State Feedback ◽

Descriptor Systems ◽

Descriptor System ◽

Linear Matrix ◽

Matrix Inequalities ◽

Control Laws ◽

Invariant Norm ◽

Norm Bound ◽

Takagi Sugeno ◽

Time Invariant

This paper focuses on the problem of Hinf control for uncertain Takagi-Sugeno fuzzy descriptor system with time-invariant norm-bound uncertainty. Sufficient condition for robust Hinf control with state feedback is derived. It is shown that the control laws can be obtained by solving a set of linear matrix inequalities (LMIs) which is numerically tractable with commercially available software. Numerical example is given to demonstrate the advantage of the proposed method.

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On Proportional Plus Derivative State Feedback H2 Control for Descriptor Systems

Handbook of Research on Advanced Intelligent Control Engineering and Automation - Advances in Computational Intelligence and Robotics ◽

10.4018/978-1-4666-7248-2.ch005 ◽

2015 ◽

pp. 146-172

Author(s):

Rim Zaghdoud ◽

Salah Salhi ◽

Moufida Ksouri

Keyword(s):

Singular Systems ◽

Descriptor Systems ◽

Linear Matrix ◽

Sufficient Condition ◽

Matrix Inequality ◽

Stable States ◽

H2 Control ◽

Closed Loop Systems ◽

Guaranteed Upper Bound ◽

Necessary And Sufficient

This chapter studies the control problem for linear singular systems. Firstly a proportional plus derivative feedback controller for continuous and discrete cases for descriptor systems is given, satisfying the closed loop systems normal and stable states. A necessary and sufficient condition for the solvability of this problem should be obtained in terms of linear matrix inequality. In second part, the designed controller is required to yield a cost function with guaranteed upper bound for the continuous and discrete case and also an extension for robust control is developed. Numerical examples are included to show the effectiveness of the proposed result.

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Robust state feedback admissibilisation of discrete linear polytopic descriptor systems: a strict linear matrix inequality approach

IET Control Theory and Applications ◽

10.1049/iet-cta.2010.0731 ◽

2012 ◽

Vol 6 (8) ◽

pp. 1097-1108 ◽

Cited By ~ 12

Author(s):

B. Sari ◽

D. Mehdi ◽

O. Bachelier

Keyword(s):

Linear Matrix Inequality ◽

State Feedback ◽

Descriptor Systems ◽

Linear Matrix ◽

Matrix Inequality ◽

Linear Matrix Inequality Approach

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Sliding mode observer based control for T-S fuzzy descriptor systems

Mathematical Foundations of Computing ◽

10.3934/mfc.2021017 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Dongyun Wang

Keyword(s):

Linear Models ◽

Sliding Mode ◽

Sliding Mode Observer ◽

Descriptor Systems ◽

Delay Systems ◽

Descriptor System ◽

Linear Matrix ◽

Matrix Inequality ◽

Integral Type ◽

Error System

<p style='text-indent:20px;'>In this paper, the problem of sliding mode observer (SMO) based sliding mode control (SMC) for nonlinear descriptor delay systems is studied. First, based on the T-S fuzzy dynamic modeling technique, the nonlinear descriptor system is transformed into a combination of local linear models. Then, a integral-type sliding surface (ITSS) based SMO is constructed for the error system. In the sequel, sufficient linear matrix inequality (LMI) conditions are established to ensure the admissibility of the sliding motions and obtain the observer gain matrix. Furthermore, two novel SMC laws are developed to ensure the reachability conditions and stabilize the descriptor systems. Finally, simulations are provided to show the effectiveness of the method.</p>

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A New Robust Training Law for Dynamic Neural Networks with External Disturbance: An LMI Approach

Discrete Dynamics in Nature and Society ◽

10.1155/2010/415895 ◽

2010 ◽

Vol 2010 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Choon Ki Ahn

Keyword(s):

Neural Networks ◽

Linear Matrix Inequality ◽

Exponential Stability ◽

External Disturbance ◽

Linear Matrix ◽

Matrix Inequality ◽

Input Output ◽

Lmi Approach ◽

Dynamic Neural Networks ◽

Numerical Examples

A new robust training law, which is called an input/output-to-state stable training law (IOSSTL), is proposed for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the IOSSTL is presented to not only guarantee exponential stability but also reduce the effect of an external disturbance. It is shown that the IOSSTL can be obtained by solving the LMI, which can be easily facilitated by using some standard numerical packages. Numerical examples are presented to demonstrate the validity of the proposed IOSSTL.

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