scholarly journals H∞ Sampled-Data Control for Singular Neutral System

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Minjie Zheng ◽  
Yujie Zhou ◽  
Shenhua Yang ◽  
Lina Li ◽  
Yongfeng Suo
Keyword(s):  
Singular System ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Neutral System ◽  
Sampled Data ◽  
Composite State ◽  
Time Varying Delay ◽  
Data Control ◽  
Conservative Result ◽  
Data Controller

This study is concerned with the H∞ control problem for singular neutral system based on sampled-data. By input delay approach and a composite state-derivative control law, the singular system is turned into a singular neutral system with time-varying delay. Less conservative result is derived for the resultant system by incorporating the delay decomposition technique, Wirtinger-based integral inequality, and an augmented Lyapunov-Krasovskii functional. Sufficient conditions are derived to guarantee that the resulting system is regular, impulse-free, and asymptotically stable with prescribed H∞ performance. Then, the H∞ sampled-data controller is designed by means of linear matrix inequalities. Finally, two simulation results have shown that the proposed method is effective.

Robust H∞ control of neutral system for sampled-data dynamic positioning ships

2018 ◽  
Vol 36 (4) ◽  
pp. 1325-1345 ◽  
Author(s):  
Minjie Zheng ◽  
Yujie Zhou ◽  
Shenhua Yang ◽  
Lina Li
Keyword(s):  
Sufficient Conditions ◽  
Control Law ◽  
Dynamic Positioning ◽  
Neutral System ◽  
Time Varying ◽  
Sampled Data ◽  
Stability Theorems ◽  
Data Control ◽  
Conservative Result ◽  
Data Controller

Abstract This study focuses on the robust ${H}_{\infty }$ sampled-data control problem of neutral system for dynamic positioning (DP) ships. Using the input delay approach and a state-derivative control law, the ship DP system is turned into a neutral system with time-varying delays. By incorporating the delay-decomposition technique, Wirtinger-based integral inequality and an augmented Lyapunov–Krasovskii functional, less conservative result is derived for the resulting system. Sufficient conditions are established to determine the system’s asymptotical stability and achieve ${H}_{\infty }$ performance using Lyapunov stability theorems. Then the ${H}_{\infty }$ sampled-data controller is obtained by analyzing the stabilization conditions. Finally, simulation result is shown that the proposed method is effective.

scholarly journals Sampled-Data Control of Singular Systems with Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Zheng Minjie ◽  
Zhou Yujie ◽  
Yang Shenhua ◽  
Li Lina
Keyword(s):  
Controller Design ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Linear Matrix ◽  
Sampled Data ◽  
Data Control ◽  
Exponentially Stable ◽  
Data Controller

This paper is concerned with sampled-data controller design for singular systems with time delay. It is assumed that the sampling periods are arbitrarily varying but bounded. A time-dependent Lyapunov function is proposed, which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals. Combining input delay approach with Lyapunov method, sufficient conditions are derived which guarante that the singular system is regular, impulse free, and exponentially stable. Then, the existence conditions of desired sampled-data controller can be obtained, which are formulated in terms of strict linear matrix inequality. Finally, numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Dissipativity-Based Reliable Sampled-Data Control With Nonlinear Actuator Faults

2016 ◽  
Vol 11 (6) ◽  
Author(s):  
Srimanta Santra ◽  
R. Sakthivel ◽  
B. Kaviarasan
Keyword(s):  
Sufficient Conditions ◽  
Control Design ◽  
Delay Systems ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Actuator Faults ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control ◽  
Data Controller

In this paper, the problem of reliable sampled-data control design with strict dissipativity for a class of linear continuous-time-delay systems against nonlinear actuator faults is studied. The main objective of this paper is to design a reliable sampled-data controller to ensure a strictly dissipative performance for the closed-loop system. Based on the linear matrix inequality (LMI) optimization approach and Wirtinger-based integral inequality, a new set of sufficient conditions is established for reliable dissipativity analysis of the considered system by assuming the mixed actuator fault matrix to be known. Then, the proposed result is extended to unknown fault matrix case. Also, the reliable sampled-data controller with strict dissipativity is designed by solving a convex optimization problem which can be easily solved by using standard numerical algorithms. Finally, a numerical example based on liquid propellant rocket motor with a pressure feeding system model is presented to illustrate the effectiveness of the developed control design technique.

Exponentially Stable Sampled-Data Control for Uncertain Systems

2014 ◽  
Vol 981 ◽  
pp. 551-554
Author(s):  
Li Ying Fan
Keyword(s):  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Control Input ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control ◽  
Exponentially Stable ◽  
Data Controller ◽  
Continuous Time System

In this paper, the problem of the exponentially stable sampled-data control was investigated for a class of uncertain systems. Based on the input delay approach, the system was modeled as a continuous-time system with the delayed control input. Attention was focused on the design of a state feedback sampled-data controller which guarantees the exponential stability of the closed-loop system for all admissible parametric uncertainties. Using linear matrix inequality (LMI) approach, sufficient conditions are obtained. Simulation example was given to demonstrate the effectiveness and correctness of the proposed method.

Robust Stochastic Sampled-Data H∞ Control for a Class of Mechanical Systems With Uncertainties

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
S. Dharani ◽  
R. Rakkiyappan ◽  
Jinde Cao
Keyword(s):  
Lyapunov Functional ◽  
Mechanical Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Sampled Data ◽  
Stiffness Matrices ◽  
Sampling Intervals ◽  
Data Controller ◽  
Wirtinger’S Inequality ◽  
Theoretical Results

This paper considers a class of mechanical systems with uncertainties appearing in all the mass, damping, and stiffness matrices. Two cases, linear fractional and randomly occurring uncertainty formulations, are considered. Since sampled-data controllers have an advantage of implementing with microcontroller or digital computer to lower the implementation cost and time, a robust stochastic sampled-data controller is considered with m sampling intervals whose occurrence probabilities are given constants and satisfy Bernoulli distribution. A discontinuous type Lyapunov functional based on the extended Wirtinger's inequality is constructed with triple integral terms and sufficient conditions that promises the robust mean square asymptotic stability of the concerned system are derived in terms of linear matrix inequalities (LMIs). In an aim to reduce the conservatism, a newly introduced concept called the second-order reciprocally convex approach is employed in deriving the bound for some cross terms that arise while maneuvering the derivative of Lyapunov functional. The obtained LMIs can be easily solved through any of the standard available software. Finally, numerical examples are given to verify the effectiveness of the proposed theoretical results.

scholarly journals State-Feedback Sampled-Data Control Design for Nonlinear Systems via Passive Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Chengming Yang ◽  
Qi Zhou ◽  
H. R. Karimi ◽  
Huanqing Wang
Keyword(s):  
Nonlinear Systems ◽  
Controller Design ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Sampled Data ◽  
Control Approach ◽  
Synthesis Conditions ◽  
Data Control ◽  
Sampled Data Control ◽  
Data Controller

This paper investigates the problem of passive controller design for a class of nonlinear systems under variable sampling. The Takagi-Sugeno (T-S) fuzzy modeling method is utilized to represent the nonlinear systems. Attention is focused on the design of passive controller for the T-S fuzzy systems via sampled-data control approach. Under the concept of very-strict passivity, a novel time-dependent Lyapunov functional is constructed to develop passive analysis criteria and passive controller synthesis conditions. A new sampled-data controller is designed to guarantee that the resulting closed-loop system is very-strictly passive. These conditions are formulated in the form of linear matrix inequalities (LMIs), which can be solved by convex optimization approach. Finally, an application example is given to demonstrate the feasibility and effectiveness of the proposed results.

Stochastic Sampled-Data Control for H∞ Stabilization of Transport Reaction Systems

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
R. Rakkiyappan ◽  
S. Dharani
Keyword(s):  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Control Input ◽  
Sampled Data ◽  
Transport Reaction ◽  
Reaction Systems ◽  
Data Control ◽  
Sampled Data Control ◽  
Discontinuous Lyapunov Functional

This paper investigates the problem of stochastic sampled-data H∞ control for a class of parabolic systems governed by one-dimensional semilinear transport reaction systems with external disturbances. A sampled-data controller design is developed by introducing the time-varying delay in the control input signals. The m sampling periods are considered whose occurrence probabilities are known constants and satisfy Bernoulli distribution. Since discontinuous Lyapunov functional copes well with problems of sampled-data control systems, a discontinuous Lyapunov functional is constructed based on the extended Wirtinger’s inequality. With this new approach, sufficient conditions that guarantee the asymptotic mean-square stabilization of the considered systems and the L2-gain analysis are derived in terms of linear matrix inequalities (LMIs), which can be solved by any of the available software.

scholarly journals Study on Bifurcation Analysis and Takagi-Sugeno Fuzzy Sampled-Data Stabilization of PMSM Systems

2021 ◽  
Author(s):  
R Vadivel ◽  
Sabarathinam Srinivasan ◽  
Yongbao Wu ◽  
NALLAPPAN GUNASEKARAN
Keyword(s):  
Fuzzy System ◽  
Permanent Magnet Synchronous Motor ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Sampled Data ◽  
Matlab Toolbox ◽  
New Class ◽  
Data Control ◽  
Delay Dependent ◽  
Takagi Sugeno

The bifurcation, stability and stabilization analysis of permanent magnet synchronous motor (PMSM) systems are investigated in this paper. To begin, a new class of delay-dependent sufficient conditions is suggested with respect to the information of the membership function, a relevant Lyapunov-Krasovskii functional (LKF), and the overall information connected with the real sampling pattern, so that the fuzzy system is ensured to be stable with a weighted dissipativity efficiency. Second, sampled-data control is intended to stabilize the Takagi-Sugeno (T-S) fuzzy system with specified integral inequalities based on the obtained results. The required conditions are stated in terms of the feasibility of linear matrix inequalities (LMIs) under the dissipativity output index, and can readily be verified by MATLAB toolbox. Finally, verification examples are contributed to demonstrated the efficacy of the techniques established in this paper.

scholarly journals TS Fuzzy Robust Sampled-Data Control for Nonlinear Systems with Bounded Disturbances

Computation ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 132
Author(s):  
Thangavel Poongodi ◽  
Prem Prakash Mishra ◽  
Chee Peng Lim ◽  
Thangavel Saravanakumar ◽  
Nattakan Boonsatit ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Fault Tolerant ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Sampled Data ◽  
Actuator Failures ◽  
Data Control ◽  
Bounded Disturbances ◽  
Delay Dependent ◽  
Takagi Sugeno

We investigate robust fault-tolerant control pertaining to Takagi–Sugeno (TS) fuzzy nonlinear systems with bounded disturbances, actuator failures, and time delays. A new fault model based on a sampled-data scheme that is able to satisfy certain criteria in relation to actuator fault matrix is introduced. Specifically, we formulate a reliable controller with state feedback, such that the resulting closed-loop-fuzzy system is robust, asymptotically stable, and able to satisfy a prescribed H∞ performance constraint. Linear matrix inequality (LMI) together with a proper construction of the Lyapunov–Krasovskii functional is leveraged to derive delay-dependent sufficient conditions with respect to the existence of robust H∞ controller. It is straightforward to obtain the solution by using the MATLAB LMI toolbox. We demonstrate the effectiveness of the control law and less conservativeness of the results through two numerical simulations.

Reliable Dissipative Sampled-Data Control for Uncertain Systems With Nonlinear Fault Input

2015 ◽  
Vol 11 (4) ◽  
Author(s):  
R. Sakthivel ◽  
S. Vimal Kumar ◽  
D. Aravindh ◽  
P. Selvaraj
Keyword(s):  
Flight Control ◽  
Linear Matrix ◽  
Sampled Data ◽  
Decomposition Approach ◽  
Data Control ◽  
Control Scheme ◽  
Special Cases ◽  
Dissipative Control ◽  
Data Controller ◽  
Delay Dependent

This paper investigates the robust reliable β-dissipative control for uncertain dynamical systems with mixed actuator faults via sampled-data approach. In particular, a more general reliable controller containing both linear and nonlinear parts is constructed for the considered system. Then, by applying the input delay approach, the sampling measurement of the digital control signal is transformed into time-varying delayed one. The aim of this paper is to design state feedback sampled-data controller to guarantee that the resulting closed-loop system to be strictly (Q, S, R)-β-dissipative. By constructing appropriate Lyapunov function and employing a delay decomposition approach, a new set of delay-dependent sufficient stabilization criteria is obtained in terms of linear matrix inequalities (LMIs). Moreover, the obtained LMIs are dependent, not only upon upper bound of time delay but also depend on the dissipative margin β and the actuator fault matrix. As special cases, H∞ and passivity control performances can be deduced from the proposed dissipative control result. Finally, numerical simulation is provided based on a flight control model to verify the effectiveness and applicability of the proposed control scheme.

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