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.

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.

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.

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.

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.

scholarly journals Observer-Based Stabilization of Spacecraft Rendezvous with Variable Sampling and Sensor Nonlinearity

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zhuoshi Li ◽  
Ming Liu ◽  
Hamid Reza Karimi ◽  
Xibin Cao
Keyword(s):  
Controller Design ◽  
Sampling Period ◽  
Controller Synthesis ◽  
Linear Matrix ◽  
Sampled Data ◽  
Closed Loop System ◽  
Unified Framework ◽  
Data Control ◽  
Variable Sampling ◽  
Exponentially Stable

This paper addresses the observer-based control problem of spacecraft rendezvous with nonuniform sampling period. The relative dynamic model is based on the classical Clohessy-Wiltshire equation, and sensor nonlinearity and sampling are considered together in a unified framework. The purpose of this paper is to perform an observer-based controller synthesis by using sampled and saturated output measurements, such that the resulting closed-loop system is exponentially stable. A time-dependent Lyapunov functional is developed which depends on time and the upper bound of the sampling period and also does not grow along the input update times. The controller design problem is solved in terms of the linear matrix inequality method, and the obtained results are less conservative than using the traditional Lyapunov functionals. Finally, a numerical simulation example is built to show the validity of the developed sampled-data control strategy.

Sampled-data control for nonlinear singular systems based on a Takagi–Sugeno fuzzy model

2018 ◽  
Vol 40 (14) ◽  
pp. 4027-4036 ◽  
Author(s):  
Zheng Minjie ◽  
Zhou Yujie ◽  
Yang Shenhua ◽  
Li Lina
Keyword(s):  
Singular Systems ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Sampled Data ◽  
Nonlinear Singular Systems ◽  
Stability Theorems ◽  
Data Control ◽  
Admissible Condition ◽  
Data Controller ◽  
Takagi Sugeno

The sampled-data admissibility problem for nonlinear singular systems in Takagi–Sugeno fuzzy models is discussed. By adding some novel terms, a novel fuzzy time-dependent Lyapunov–Krasovskii functional is proposed to fully capture the available characteristics of the actual sampling pattern. Sufficient conditions are derived to determine the regularity, absence of impulses and asymptotic stability of the system by using Lyapunov stability theorems. Then, the fuzzy sampled-data controller is obtained by analysing the admissible condition. One practical example involving a truck–trailer system is considered. It is shown that the proposed method and the designed controller for the system are effective and that less conservativeness can be obtained.

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 Stability and Stabilization of Continuous-Time Markovian Jump Singular Systems with Partly Known Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jumei Wei ◽  
Rui Ma
Keyword(s):  
Continuous Time ◽  
Controller Design ◽  
Partial Information ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
The Stability

This paper investigates the problem of the stability and stabilization of continuous-time Markovian jump singular systems with partial information on transition probabilities. A new stability criterion which is necessary and sufficient is obtained for these systems. Furthermore, sufficient conditions for the state feedback controller design are derived in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.

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.

Synchronization for hybrid coupled reaction-diffusion neural networks with stochastic disturbances via spatial sampled-data control strategy

2020 ◽  
pp. 095965182093566
Author(s):  
Xiaona Song ◽  
Xingru Li ◽  
Zhaoke Ning ◽  
Mi Wang ◽  
Jingtao Man
Keyword(s):  
Neural Networks ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Coupling Reaction ◽  
Reaction Diffusion ◽  
Sampled Data ◽  
Stochastic Disturbances ◽  
Digital Controllers ◽  
Data Control ◽  
Sampled Data Control

The synchronization of reaction-diffusion neural networks with state and spatial couplings is investigated in this article, and the time-varying delay and stochastic disturbances are considered in the proposed systems. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Here, we suggest a spatial sampled-data controller design, where the sampled-data (in space) measurements of the state are taken in a finite number of fixed sampling points in the spatial domain. It is assumed that the sampling intervals in space are bounded. Based on the Lyapunov stability theory, Young’s and Wirtinger’s inequalities techniques, some sufficient conditions are presented to synchronize the hybrid coupling reaction-diffusion neural networks with stochastic disturbances. Finally, the efficiency of the derived criteria will be demonstrated by resorting to two numerical examples.

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