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.

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 Delay-Dependent RobustH∞Filtering of the Takagi-Sugeno Fuzzy Stochastic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Ze Li ◽  
Xin-Hao Yang
Keyword(s):  
Stochastic Systems ◽  
Design Method ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Mean Square Stability ◽  
Error System ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper is concerned with the problem of the robustH∞filtering for the Takagi-Sugeno (T-S) fuzzy stochastic systems with bounded parameter uncertainties. For a given T-S fuzzy stochastic system, this paper focuses on the stochastically mean-square stability of the filtering error system and theH∞performance level of the output error and the disturbance input. The design method for delay-dependent filter is developed based on linear matrix inequalities. Finally, the effectiveness of the proposed methods is substantiated with an illustrative example.

scholarly journals Gain scheduled controller design for thermo-optical plant

2014 ◽  
Vol 24 (3) ◽  
pp. 333-349 ◽  
Author(s):  
Vojtech Veselý ◽  
Jakub Osuský ◽  
Ivan Sekaj
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Design Method ◽  
Feedback Gain ◽  
Small Gain ◽  
Gain Scheduled Controller ◽  
The Stability ◽  
Gain Scheduled ◽  
Siso Systems

Abstract This paper presents a gain scheduled controller design for MIMO and SISO systems in the frequency domain using the genetic algorithms approach. The proposed method is derived from the M-delta structure of closed loop MIMO (SISO) systems and the small gain theory is exploited to obtain the stability condition. An example of real system illustrates the effectiveness of the proposed output feedback gain scheduled controller design method and also the possibility to improve its performance using the genetic algorithm

ROBUST EXPONENTIAL STABILITY OF STOCHASTIC TIME-DELAY SYSTEMS WITH UNCERTAINTIES AND NONLINEAR PERTURBATIONS

2009 ◽  
Vol 06 (01) ◽  
pp. 61-71 ◽  
Author(s):  
HUAICHENG YAN ◽  
MAX Q.-H. MENG ◽  
XINHAN HUANG ◽  
HAO ZHANG
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Mean Square ◽  
Nonlinear Perturbations ◽  
Robust Exponential Stability ◽  
Mean Square Stability ◽  
Delay Dependent

In this paper, the delay-dependent robust exponential mean-square stability analysis problem is considered for a class of uncertain stochastic systems with time-varying delay and nonlinear perturbations. Some sufficient conditions on delay-dependent robust exponential stability in the mean square are established in terms of linear matrix inequalities (LMIs) by exploiting a novel Lyapunov–Krasovskii functional and by making use of zero equations methods. These developed results indicate less conservatism than the existing ones due to the introduction of some free weighting matrices which can be selected properly. The new delay-dependent stability criteria are expressed as a set of LMIs, which can be readily solved by using standard numerical software. Numerical examples are provided to demonstrate the effectiveness and the applicability of the proposed criteria.

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.

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 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 Suboptimal Disturbance Observer Design Using All Stabilizing Q Filter for Precise Tracking Control

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1434 ◽  
Author(s):  
Wonhee Kim ◽  
Sangmin Suh
Keyword(s):  
Design Method ◽  
Industrial Applications ◽  
Point Of View ◽  
Observer Design ◽  
Linear Matrix ◽  
External Disturbances ◽  
Closed Loop Systems ◽  
Control Target ◽  
The Stability ◽  
Unified Index

For several decades, disturbance observers (DOs) have been widely utilized to enhance tracking performance by reducing external disturbances in different industrial applications. However, although a DO is a verified control structure, a conventional DO does not guarantee stability. This paper proposes a stability-guaranteed design method, while maintaining the DO structure. The proposed design method uses a linear matrix inequality (LMI)-based H∞ control because the LMI-based control guarantees the stability of closed loop systems. However, applying the DO design to the LMI framework is not trivial because there are two control targets, whereas the standard LMI stabilizes a single control target. In this study, the problem is first resolved by building a single fictitious model because the two models are serial and can be considered as a single model from the Q-filter point of view. Using the proposed design framework, all-stabilizing Q filters are calculated. In addition, for the stability and robustness of the DO, two metrics are proposed to quantify the stability and robustness and combined into a single unified index to satisfy both metrics. Based on an application example, it is verified that the proposed method is effective, with a performance improvement of 10.8%.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

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