scholarly journals Stability Criterion of Linear Stochastic Systems Subject to MixedH2/PassivityPerformance

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Cheung-Chieh Ku ◽  
Chih-Peng Lu ◽  
Min-Ta Li
Keyword(s):  
Stability Criterion ◽  
Stochastic Systems ◽  
Initial Conditions ◽  
Design Method ◽  
External Disturbance ◽  
Sufficient Conditions ◽  
Asymptotical Stability ◽  
Linear Matrix ◽  
Generator System ◽  
Control Scheme

TheH2control scheme and passivity theory are applied to investigate the stability criterion of continuous-time linear stochastic system subject to mixed performance. Based on the stochastic differential equation, the stochastic behaviors can be described as multiplicative noise terms. For the considered system, theH2control scheme is applied to deal with the problem on minimizing output energy. And the asymptotical stability of the system can be guaranteed under desired initial conditions. Besides, the passivity theory is employed to constrain the effect of external disturbance on the system. Moreover, the Itô formula and Lyapunov function are used to derive the sufficient conditions which are converted into linear matrix inequality (LMI) form for applying convex optimization algorithm. Via solving the sufficient conditions, the state feedback controller can be established such that the asymptotical stability and mixed performance of the system are achieved in the mean square. Finally, the synchronous generator system is used to verify the effectiveness and applicability of the proposed design method.

Delay-Dependent Robust Control for Discrete-Time Uncertain Stochastic Systems With Time-Varying Delays

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Cheung-Chieh Ku ◽  
Guan-Wei Chen
Keyword(s):  
Robust Control ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Gain Scheduled Controller ◽  
Delay Dependent

This paper investigates a delay-dependent robust control problem of discrete-time uncertain stochastic systems with delays. The uncertainty considered in this paper is time-varying but norm-bounded, and the delays are considered as interval time-varying case for both state and input. According to the considerations of uncertainty, stochastic behavior, and time delays, the problem considered in this paper is more general than the existing works for uncertain stochastic systems. Via the proposed Lyapunov–Krasovskii function, some sufficient conditions are derived into the extended linear matrix inequality form. Moreover, Jensen inequality and free matrix equation are employed to reduce conservatism of those conditions. Through using the proposed design method, a gain-scheduled controller is designed to guarantee asymptotical stability of uncertain stochastic systems in the sense of mean square. Finally, two numerical examples are provided to demonstrate applicability and effectiveness of the proposed design method.

scholarly journals Fuzzy Static Output Control of T-S Fuzzy Stochastic Systems via Line Integral Lyapunov Function

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 697
Author(s):  
Cheung-Chieh Ku ◽  
Yun-Chen Yeh ◽  
Yann-Hong Lin ◽  
Yu-Yen Hsieh
Keyword(s):  
Lyapunov Function ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Nonlinear Stochastic Systems ◽  
Line Integral ◽  
Output Control ◽  
Static Output

Considering some unmeasurable states, a fuzzy static output control problem of nonlinear stochastic systems is discussed in this paper. Based on a modelling approach, a Takagi–Sugeno (T–S) fuzzy system, constructed by a family of stochastic differential equations and membership functions, is applied to represent nonlinear stochastic systems. Parallel distributed compensation (PDC) technology is used to construct the static output controller. A line-integral Lyapunov function (LILF) is used to derive some sufficient conditions for guaranteeing the asymptotical stability in the mean square. From the LILF, a potential conservatism produced by the derivative of the membership function is eliminated to increase the relaxation of sufficient conditions. Furthermore, those conditions are transferred into linear matrix inequality (LMI) form via projection lemma. According to the convex optimization algorithm, the feasible solutions are directly obtained to establish the static output fuzzy controller. Finally, a numerical example is applied to demonstrate the effectiveness and usefulness of the proposed design method.

scholarly journals H∞Gain-Scheduled Control for LPV Stochastic Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Cheung-Chieh Ku ◽  
Guan-Wei Chen
Keyword(s):  
Stochastic Systems ◽  
Weighting Function ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Mean Square ◽  
Gain Scheduled Controller ◽  
The Stability ◽  
Uncertain Stochastic System ◽  
Gain Scheduled

A robust control problem for discrete-time uncertain stochastic systems is discussed via gain-scheduled control scheme subject toH∞attenuation performance. Applying Linear Parameter Varying (LPV) modeling approach and stochastic difference equation, the uncertain stochastic systems can be described by combining time-varying weighting function and linear systems with multiplicative noise terms. Due to the consideration of stochastic behavior, the stability in the sense of mean square is applied for the system. Furthermore, two kinds of Lyapunov functions are employed to derive their corresponding sufficient conditions to solve the stabilization problems of this paper. In order to use convex optimization algorithm, the derived conditions are converted into Linear Matrix Inequality (LMI) form. Via solving those conditions, the gain-scheduled controller can be established such that the robust asymptotical stability andH∞performance of the disturbed uncertain stochastic system can be achieved in the sense of mean square. Finally, two numerical examples are applied to demonstrate the effectiveness and applicability of the proposed design method.

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.

Vibration control of network-based offshore structures subject to earthquakes

2021 ◽  
pp. 014233122110259
Author(s):  
Hua-Nv Feng ◽  
Bao-Lin Zhang ◽  
Yan-Dong Zhao ◽  
Hui Ma ◽  
Hao Su ◽  
...  
Keyword(s):  
Sufficient Conditions ◽  
Offshore Structures ◽  
Delay Systems ◽  
Linear Matrix ◽  
Seismic Responses ◽  
Marine Structures ◽  
Damping Control ◽  
Marine Structure ◽  
Uncertain Model ◽  
Control Scheme

Marine structures are inevitably influenced by parametric perturbations as well as multiple external loadings. Among these loadings, earthquake is generally more destructive and unpredictable than others. It is significant to develop effective active control schemes to guarantee the safety, stability, and integrity of marine structures subject to earthquakes and parametric perturbations. In this paper, the problem of networked [Formula: see text] robust damping control is addressed to stabilize a marine structure subject to earthquakes. First, in consideration of perturbations of the structure parameters, an uncertain model of the networked marine structure under earthquakes is presented. Second, a robust networked [Formula: see text] control scheme is presented to suppress seismic responses of the structure. By using stability theory of time-delay systems, several sufficient conditions on robust stability of the networked marine structure system are obtained, and the linear matrix inequality methods are utilized to solve the gain matrix of the controller. Finally, simulation indicates that compared with the traditional robust [Formula: see text] control and the proposed networked [Formula: see text] control, the seismic responses amplitudes of the marine structure under the two controllers are almost the same, while the latter is more economic than the former.

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.

scholarly journals Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ze Tang ◽  
Jianwen Feng
Keyword(s):  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Control Cost ◽  
Synchronization Problem ◽  
Delayed Coupling ◽  
Control Scheme ◽  
Successful Control ◽  
Synchronization Pattern

We focus on the cluster synchronization problem for a kind of general networks with nondelayed and delayed coupling. Based on the pinning control scheme, a small fraction of the nodes in each cluster are pinned for successful control, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the cluster synchronization pattern for all initial values by means of the Lyapunov stability theorem and linear matrix inequalities (LMIs). By using the adaptive update law, relative smaller control gains are obtained, and hence the control cost can be substantially lower. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.

scholarly journals H∞ Filtering for Discrete-Time Nonlinear Singular Systems with Quantization

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Yifu Feng ◽  
Zhi-Min Li ◽  
Xiao-Heng Chang
Keyword(s):  
Discrete Time ◽  
Filter Design ◽  
Design Method ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Nonlinear Singular Systems ◽  
Attenuation Level ◽  
Measurement Output

This paper investigates the problem of H∞ filtering for class discrete-time Lipschitz nonlinear singular systems with measurement quantization. Assume that the system measurement output is quantized by a static, memoryless, and logarithmic quantizer before it is transmitted to the filter, while the quantizer errors can be treated as sector-bound uncertainties. The attention of this paper is focused on the design of a nonlinear quantized H∞ filter to mitigate quantization effects and ensure that the filtering error system is admissible (asymptotically stable, regular, and causal), while having a unique solution with a prescribed H∞ noise attenuation level. By introducing some slack variables and using the Lyapunov stability theory, some sufficient conditions for the existence of the nonlinear quantized H∞ filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to demonstrate the effectiveness of the proposed quantized filter design method.

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