scholarly journals Finite-Time Admissibility and Controller Design for T-S Fuzzy Stochastic Singular Systems with Distinct Differential Term Matrices

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Liang Qiao ◽  
Zhaomin Lv
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Controller Design ◽  
Design Method ◽  
Singular Systems ◽  
Linear Matrix ◽  
Fuzzy Membership Functions ◽  
Fuzzy Lyapunov Function ◽  
Parameter Perturbations ◽  
Stochastic Singular Systems

The finite-time admissibility analysis and controller design issues for extended T-S fuzzy stochastic singular systems (FSSSs) with distinct differential term matrices and Brownian parameter perturbations are discussed. When differential term matrices are allowed to be distinct in fuzzy rules, such fuzzy models can describe a wide class of nonlinear stochastic systems. Using fuzzy Lyapunov function (FLF), a new and relaxed sufficient condition is proposed via strict linear matrix inequalities (LMIs). Different from the existing stability conditions by FLF, the derivative bounds of fuzzy membership functions are not required in this condition. Based on admissibility analysis results, a design method for parallel distribution compensation (PDC) controller of FSSSs is given to guarantee the finite-time admissibility of the closed-loop system. Finally, the feasibility and effectiveness of the proposed methods in this article are illustrated with three examples.

Finite-time guaranteed cost controller design for uncertain linear continuous-time singular systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3507-3515 ◽  
Author(s):  
Bo Li ◽  
Songlin Wo ◽  
Junjie Zhao ◽  
Xuejing Ren
Keyword(s):  
Continuous Time ◽  
Finite Time ◽  
Closed Loop ◽  
Controller Design ◽  
Singular Systems ◽  
Singular System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Guaranteed Cost ◽  
Bounded Uncertainties

This article concerns the finite-time robust guaranteed cost control problem for a class of linear continuous-time singular systems with norm-bounded uncertainties. In this study, the problem is to design a state feedback controller such that the closed-loop system is finite-time stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. By constructing an appropriate Lyapunov function, a sufficient condition for the finite-time robust stability of the system based on linear matrix inequality (LMI) is established. Furthermore, the sufficient condition for the existence of the guaranteed cost controller is formulated in terms of LMIs, which can make the closed-loop uncertain singular system finite-time robust stable. Finally, two numerical examples are given for illustration of the proposed theoretical results.

Admissible Finite-Time Stability and Stabilization of Uncertain Discrete Singular Systems

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Wenping Xue ◽  
Weijie Mao
Keyword(s):  
Finite Time ◽  
Controller Design ◽  
Singular Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Stability ◽  
Finite Time Stability ◽  
Fixed Parameter ◽  
Discrete Singular Systems ◽  
Definition Of

The problems of admissible finite-time stability (AFTS) and admissible finite-time stabilization for a class of uncertain discrete singular systems are addressed in this study. The definition of AFTS is first given. Second, a sufficient condition for the AFTS of the nominal unforced system is established, which is further extended to the uncertain case. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is admissibly finite-time stable for all admissible uncertainties. Both the AFTS and the controller design conditions are presented in terms of linear matrix inequalities (LMIs) with a fixed parameter. Finally, two numerical examples are provided to illustrate the effectiveness of the developed theory.

scholarly journals Reliablel2–l∞andH∞Control for Nonlinear Singular Systems via Dynamic Output Feedback

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lin Li ◽  
Yuting Kang
Keyword(s):  
Controller Design ◽  
Design Method ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Dynamic Feedback ◽  
Nonlinear Controller ◽  
Dynamic Feedback Control ◽  
Disturbance Attenuation Level

The reliablel2–l∞andH∞control for a class of Lipschitz nonlinear discrete-time singular systems with time delay is investigated via dynamic feedback control. The main goal of this paper is to design a generalized nonlinear controller such that, for possible actuator failures, the closed-loop system is regular, casual, and stable with a givenl2–l∞andH∞disturbance attenuation level being satisfied. Some sufficient conditions are obtained in terms of linear matrix inequalities (LMIs), and the controller design method is also proposed. Finally, a numerical example is included to illustrate the effectiveness of our proposed results.

Finite-time bounded control design for one-sided Lipschitz differential inclusions

2020 ◽  
pp. 095965182095883
Author(s):  
Chenglai Zhou ◽  
Ping He ◽  
Heng Li ◽  
Zuxin Li ◽  
Zhouchao Wei ◽  
...  
Keyword(s):  
Linear Matrix Inequality ◽  
Finite Time ◽  
Differential Inclusions ◽  
Controller Design ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Bounded Control ◽  
Initial State

This article considers finite-time bounded controller design for one-sided Lipschitz nonlinear differential inclusions. Sufficient conditions of finite-time bounded criterion are given employing convex hull Lyapunov function approach. An algorithm is designed to calculate the finite-time bounded controller. Moreover, a system initial state selection method is presented to find the domain of system initial state aid for transforming quasi-linear matrix inequality–based conditions to linear matrix inequality-based conditions. Finally, a numerical example and a comparison experiment example are given to illustrate the effectiveness of this proposed design method.

scholarly journals Robust Finite-Timeℋ∞Control for Uncertain Systems Subject to Intermittent Measurements

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zhenghong Deng
Keyword(s):  
Finite Time ◽  
Controller Design ◽  
Design Method ◽  
Design Procedure ◽  
Linear Matrix ◽  
Finite Time Stability ◽  
System A ◽  
Controller Gain ◽  
Intermittent Measurements ◽  
Time Systems

This paper investigates the robust finite-timeℋ∞controller design problem of discrete-time systems with intermittent measurements. It is assumed that the system is subject to the norm-bounded uncertainties and the measurements are intermittent. The Bernoulli process is used to describe the phenomenon of intermittent measurements. By substituting the state-feedback controller into the system, a stochastic closed-loop system is obtained. Based on the analysis of the robust stochastic finite-time stability and theℋ∞performance, the controller design method is proposed. The controller gain can be calculated by solving a sequence of linear matrix inequalities. Finally, a numerical example is used to show the design procedure and the effectiveness of the proposed design methodology.

Gain-Scheduled H∞ Control for Linear Parameter Varying Stochastic Systems

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Cheung-Chieh Ku ◽  
Cheng-I Wu
Keyword(s):  
Stochastic Systems ◽  
Controller Design ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying ◽  
Gain Scheduled Controller ◽  
Gain Scheduled

In this paper, a gain-scheduled controller design method is proposed for linear parameter varying (LPV) stochastic systems subject to H∞ performance constraint. Applying the stochastic differential equation, the stochastic behaviors of system are described via multiplicative noise terms. Employing the gain-scheduled design technique, the stabilization problem of LPV stochastic systems is discussed. Besides, the H∞ attenuation performance is employed to constrain the effect of external disturbance. Based on the Lyapunov function and Itô's formula, the sufficient conditions are derived to propose the stability criteria for LPV stochastic systems. The derived sufficient conditions are converted into linear matrix inequality (LMI) problems that can be solved by using convex optimization algorithm. Through solving these conditions, the gain-scheduled controller can be obtained to guarantee asymptotical stability and H∞ performance of LPV stochastic systems. Finally, numerical examples are provided to demonstrate the applications and effectiveness of the proposed controller design method.

scholarly journals Robust H∞-Control for Uncertain Stochastic Systems with Impulsive Effects

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1169
Author(s):  
Zhezhe Xin ◽  
Chunjie Xiao ◽  
Ting Hou ◽  
Xiao Shen
Keyword(s):  
Linear Matrix Inequalities ◽  
Uncertain Systems ◽  
Stochastic Systems ◽  
Controller Design ◽  
Design Method ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Stochastic Effects

Robust stabilization and H ∞ controller design for uncertain systems with impulsive and stochastic effects have been deeply discussed. Some sufficient conditions for the considered system to be robustly stable are derived in terms of linear matrix inequalities (LMIs). In addition, an example with simulations is given to better demonstrate the usefulness of the proposed H ∞ controller design method.

scholarly journals Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback Scheme

2021 ◽  
Vol 11 (6) ◽  
pp. 2833
Author(s):  
Wen-Jer Chang ◽  
Ming-Hsuan Tsai ◽  
Chin-Lin Pen
Keyword(s):  
Discrete Time ◽  
Control Method ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Design Method ◽  
Singular Systems ◽  
Lyapunov Theory ◽  
Linear Matrix ◽  
Feedback Scheme ◽  
The Stability

This paper investigates the observer-based fuzzy controller design method for nonlinear discrete-time singular systems that are represented by Takagi-Sugeno (T-S) fuzzy models. At first, the nonlinearity can be well-approximated with several local linear input-output relationships. The parallel distributed compensation (PDC) technology and the proportional derivative (PD) feedback scheme are then employed to construct the observer-based fuzzy controller. To solve the problem of unmeasured states, the impulsive phenomenon of singular systems, and the PD scheme’s reasonableness, a novel observer-based fuzzy controller is developed. By using the Lyapunov theory and projection lemma, the stability criteria are built in terms of linear matrix inequalities (LMI). Moreover, the gains of fuzzy controller and fuzzy observer can be calculated synchronously by using convex optimization algorithms. Finally, a biological economic system is provided to verify the effectiveness of the proposed fuzzy control method.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

scholarly journals Finite-Time Stabilization for Stochastic Inertial Neural Networks with Time-Delay via Nonlinear Delay Controller

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Deyi Li ◽  
Yuanyuan Wang ◽  
Guici Chen ◽  
Shasha Zhu
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Finite Time ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Feedback ◽  
Inertial Neural Networks ◽  
Finite Time Stabilization

This paper pays close attention to the problem of finite-time stabilization related to stochastic inertial neural networks with or without time-delay. By establishing proper Lyapunov-Krasovskii functional and making use of matrix inequalities, some sufficient conditions on finite-time stabilization are obtained and the stochastic settling-time function is also estimated. Furthermore, in order to achieve the finite-time stabilization, both delayed and nondelayed nonlinear feedback controllers are designed, respectively, in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the correction of the theoretical results and the effectiveness of the proposed control design method.

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