scholarly journals On an Application of the Absolute Stability Theory to Sampled-Data Stabilization

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Alexander N. Churilov
Keyword(s):  
Closed Loop ◽  
Control Function ◽  
Linear Matrix ◽  
Feedback Signal ◽  
Matrix Inequality ◽  
Sampled Data ◽  
Closed Loop System ◽  
The Stability ◽  
Absolute Stability Theory ◽  
Sampling Times

A nonlinear Lur’e-type plant with a sector bound nonlinearity is considered. The plant is stabilized by a discrete-time feedback signal with a nonperiodic uncertain sampling. The sampling control function is nonlinear and also obeys some sectoral constraints at discrete (sampling) times. The linear matrix inequality (LMI) conditions for the stability of the closed-loop system are obtained.

scholarly journals Robust LFC Strategy for Wind Integrated Time-Delay Power System Using EID Compensation

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3223 ◽  
Author(s):  
Liu ◽  
Zhang ◽  
Zou
Keyword(s):  
Time Delay ◽  
Power System ◽  
Closed Loop ◽  
Frequency Control ◽  
Loop System ◽  
Load Frequency Control ◽  
System Stability ◽  
Linear Matrix ◽  
Closed Loop System ◽  
The Stability

This paper presents an active disturbance rejection control (ADRC) technique for load frequency control of a wind integrated power system when communication delays are considered. To improve the stability of frequency control, equivalent input disturbances (EID) compensation is used to eliminate the influence of the load variation. In wind integrated power systems, two area controllers are designed to guarantee the stability of the overall closed-loop system. First, a simplified frequency response model of the wind integrated time-delay power system was established. Then the state-space model of the closed-loop system was built by employing state observers. The system stability conditions and controller parameters can be solved by some linear matrix inequalities (LMIs) forms. Finally, the case studies were tested using MATLAB/SIMULINK software and the simulation results show its robustness and effectiveness to maintain power-system stability.

scholarly journals Stability of Sampled-Data Control for Lurie Systems with Slope-Restricted Nonlinearities

2020 ◽  
Author(s):  
Mathias Giordani Titton ◽  
João Manoel Gomes da Silva Jr. ◽  
Giórgio Valmórbida
Keyword(s):  
Continuous Time ◽  
Optimization Problems ◽  
Linear Matrix ◽  
Sampled Data ◽  
Closed Loop System ◽  
Integral Term ◽  
New Class ◽  
Data Control ◽  
The Stability ◽  
Continuous Time System

This paper deals with the stability analysis of aperiodic sampled-data Lurie systems, where the nonlinearity is assumed to be both sector and slope restricted. The proposed method is based on the use of a new class of looped-functionals whose derivative is negative along the trajectories of the continuous-time system. In addition, it contains a generalized Lurie-type function that is quadratic on both the states and the nonlinearity and has a Lurie-Postnikov integral term, which provides some advantages in comparison to simpler candidate functions. On this basis, stability conditions in the form of linear matrix inequalities (LMIs) are formulated. It is shown that the proposed conditions guarantee that the Lurie function is strictly decreasing at the sampling instants, which also implies that the continuous-time trajectories converge asymptotically to the origin. We then formulate some optimization problems for computing themaximal intersampling interval or the maximal sector bounds for which the stability of the sampled-data closed-loop system is guaranteed. A numerical example to illustrate the results is provided.

scholarly journals Stability Analysis of Networked Control System Using LMI Approach

2018 ◽  
Vol 7 (2.31) ◽  
pp. 249
Author(s):  
Richa Sharma ◽  
Deepak Nagaria
Keyword(s):  
Communication Network ◽  
Control System ◽  
Closed Loop ◽  
Sampling Period ◽  
Networked Control System ◽  
Networked Control ◽  
Linear Matrix ◽  
Matlab Simulation ◽  
Closed Loop System ◽  
The Stability

Networked control system is a closed loop system in which information or data travel through the communication network. The presence of communication network will increase time delay and information losses. Due to these losses and delay the performance of the system decreases. This paper represents an analysis to find the stability of the networked control system with the varying time hindrances present in the network. In this research, it has been assumed that the delay in time is less than the sampling period. The stability conditions for NCS have been procured with the use of the Lyapunov function approach and has been described in terms of LMI(Linear Matrix Inequality).This examination confirm the adequate state of stability through MATLAB simulation and the numerical case demonstrates the outcome.  

A Novel Delay-Independent Robust Adaptive Controller Design for Uncertain Nonlinear Systems With Time-Varying State Delay

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Hadi Azmi ◽  
Alireza Yazdizadeh
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Closed Loop ◽  
Controller Design ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
System Delay ◽  
Closed Loop System

Abstract In this paper, two novel adaptive control strategies are presented based on the linear matrix inequality for nonlinear Lipschitz systems. The proposed approaches are developed by creatively using Krasovskii stability theory to compensate parametric uncertainty, unknown time-varying internal delay, and bounded matched or mismatched disturbance effects in closed-loop system of nonlinear systems. The online adaptive tuning controllers are designed such that reference input tracking and asymptotic stability of the closed-loop system are guaranteed. A novel structural algorithm is developed based on linear matrix inequality (LMI) and boundaries of the system delay or uncertainty. The capabilities of the proposed tracking and regulation methods are verified by simulation of three physical uncertain nonlinear system with real practical parameters subject to internal or state time delay and disturbance.

Controller Design and Stability Analysis of Output Pressure Regulation in Electrohydrostatic Actuators

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Masoumeh Esfandiari ◽  
Nariman Sepehri
Keyword(s):  
Closed Loop ◽  
Open Loop ◽  
Loop System ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Closed Loop System ◽  
Output Pressure ◽  
Frequency Responses ◽  
Wide Range ◽  
The Stability

In this paper, a robust fixed-gain linear output pressure controller is designed for a double-rod electrohydrostatic actuator using quantitative feedback theory (QFT). First, the family of frequency responses of the system is identified by applying an advanced form of fast Fourier transform on the open-loop input–output experimental data. This approach results in realistic frequency responses of the system, which prevents the generation of unnecessary large QFT templates, and consequently contributes to the design of a low-order QFT controller. The designed controller provides desired transient responses, desired tracking bandwidth, robust stability, and disturbance rejection for the closed-loop system. Experimental results confirm the desired performance met by the QFT controller. Then, the nonlinear stability of the closed-loop system is analyzed considering the friction and leakage, and in the presence of parametric uncertainties. For this analysis, Takagi–Sugeno (T–S) fuzzy modeling and its stability theory are employed. The T–S fuzzy model is derived for the closed-loop system and the stability conditions are presented as linear matrix inequalities (LMIs). LMIs are found feasible and thus the stability of the closed-loop system is proven for a wide range of parametric uncertainties and in the presence of friction and leakages.

Sampled-data mixed H∞ and passive control for attitude stabilization and vibration suppression of flexible spacecrafts with input delay

2018 ◽  
Vol 24 (22) ◽  
pp. 5401-5417 ◽  
Author(s):  
Baolong Zhu ◽  
Zhiping Zhang ◽  
Mingliang Suo ◽  
Ying Chen ◽  
Shunli Li
Keyword(s):  
Closed Loop ◽  
Passive Control ◽  
Vibration Suppression ◽  
Design Method ◽  
Performance Criterion ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Sampled Data ◽  
Closed Loop System

This paper deals with the problem of mixed [Formula: see text] and passive control for flexible spacecrafts subject to nonuniform sampling and time-varying delay in the input channel. An impulsive observer-based controller is introduced and the resulting closed-loop system is a hybrid system consisting of a continuous time-delay subsystem and an impulsive differential subsystem. As a first result, we derive a generalized bounded real lemma (GBRL), that is, a generalized [Formula: see text] performance criterion, for the impulsive differential subsystem by constructing a time-varying Lyapunov functional. Then, on the basis of this GBRL and utilizing the Lyapunov–Krasovskii approach, a sufficient condition is derived to asymptotically stabilize the closed-loop system and simultaneously guarantee a prescribed mixed [Formula: see text] and passivity performance index. A design method is proposed for the desired controller, which can be readily constructed by solving a convex optimization problem with linear matrix inequalities (LMIs) constraints. Finally, numerical experiments are provided to support the theoretical results, and comparisons with former approaches are also discussed.

Adaptive attitude-tracking control of spacecraft considering on-orbit refuelling

2020 ◽  
pp. 014233122097313
Author(s):  
Yiqi Xu
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Closed Loop System ◽  
Tracking Errors ◽  
Attitude Tracking ◽  
Control Scheme ◽  
Inertia Model ◽  
And Performance ◽  
Attitude Tracking Control ◽  
The Stability

This paper studies the attitude-tracking control problem of spacecraft considering on-orbit refuelling. A time-varying inertia model is developed for spacecraft on-orbit refuelling, which actually includes two processes: fuel in the transfer pipe and fuel in the tank. Based upon the inertia model, an adaptive attitude-tracking controller is derived to guarantee the stability of the resulted closed-loop system, as well as asymptotic convergence of the attitude-tracking errors, despite performing refuelling operations. Finally, numerical simulations illustrate the effectiveness and performance of the proposed control scheme.

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.

scholarly journals Design of delay observer-based controllers for uncertain time-lag systems

1999 ◽  
Vol 5 (2) ◽  
pp. 121-137 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Mohamed Zribi
Keyword(s):  
Uncertain Systems ◽  
Closed Loop ◽  
Time Lag ◽  
Linear Matrix ◽  
Time Lags ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Delayed Measurements ◽  
Uncertain Time ◽  
Theoretical Developments

In this paper, the problem of designing observers and observer-based controllers for a class of uncertain systems with input and state time lags is considered. We construct delay-type observers in which both the instantaneous as well as the delayed measurements are utilized. Using feedback control based on the reconstructed state, the behavior of the closed-loop system is investigated. It is established that the uncertain time-lag system with delay observer-based control is asymptotically stable. Expressions for the gain matrices are given based on two linear-matrix inequalities. A numerical example is given to illustrate the theoretical developments.

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