scholarly journals RobustH∞Control for Discrete-Time Stochastic Interval System with Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Shengchun Yu ◽  
Guici Chen ◽  
Yi Shen
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Delay System ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Time Delay System ◽  
Interval System ◽  
Uncertain Time ◽  
System With Time Delay

The robustH∞control problem for discrete-time stochastic interval system (DTSIS) with time delay is investigated in this paper. The stochastic interval system is equivalently transformed into a kind of stochastic uncertain time-delay system firstly. By constructing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions for the existence of the robustH∞controller for DTSIS are obtained in terms of linear matrix inequality (LMI) form, and the robustH∞controller is designed. Finally, a numerical example with simulation is given to show the effectiveness and correctness of the designed robustH∞controller.

scholarly journals Passivity analysis and synthesis for uncertain time-delay systems

2001 ◽  
Vol 7 (5) ◽  
pp. 455-484 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Lihua Xie
Keyword(s):  
Time Delay ◽  
Design Method ◽  
Delay System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Time Delay System ◽  
Passivity Analysis ◽  
Analysis And Synthesis ◽  
Uncertain Time

In this paper, we investigate the robust passivity analysis and synthesis problems for a class of uncertain time-delay systems. This class of systems arises in the modelling effort of studying water quality constituents in fresh stream. For the analysis problem, we derive a sufficient condition for which the uncertain time-delay system is robustly stable and strictly passive for all admissible uncertainties. The condition is given in terms of a linear matrix inequality. Both the delay-independent and delay-dependent cases are considered. For the synthesis problem, we propose an observer-based design method which guarantees that the closed-loop uncertain time-delay system is stable and strictly passive for all admissible uncertainties. Several examples are worked out to illustrate the developed theory.

scholarly journals Discrete-Time Sliding Mode Control for Uncertain Networked System Subject to Time Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Saulo C. Garcia ◽  
Marcelo C. M. Teixeira ◽  
José Paulo F. Garcia ◽  
Uiliam N. L. T. Alves ◽  
Jean M. S. Ribeiro
Keyword(s):  
Time Delay ◽  
Sliding Mode Control ◽  
Discrete Time ◽  
Uncertain Systems ◽  
Sliding Mode ◽  
Delay System ◽  
Control Law ◽  
Time Delay System ◽  
Mode Control ◽  
Uncertain Time

We deal with uncertain systems with networked sliding mode control, subject to time delay. To minimize the degenerative effects of the time delay, a simpler format of state predictor is proposed in the control law. Some ultimate bounded stability analyses and stabilization conditions are provided for the uncertain time delay system with proposed discrete-time sliding mode control strategy. A numerical example is presented to corroborate the analyses.

Robust Predictive Control for Uncertain Time-Delay Systems with Nonlinear Disturbance

2012 ◽  
Vol 490-495 ◽  
pp. 1496-1500
Author(s):  
Jia Cheng Zhao ◽  
Cheng Li Su ◽  
Ping Li
Keyword(s):  
Time Delay ◽  
Predictive Control ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Delay System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Stable Theory ◽  
Uncertain Time ◽  
Control Principle

Based on predictive control principle of receding optimization, the infinite time domain “min-max” optimization problems are converted into convex programming problems by Lyapunov stable theory and linear matrix inequality (LMI). The sufficient conditions for the robust stability of the uncertain time-delay system are given. Finally, the simulation results illustrate the effectiveness of the proposed methods.

scholarly journals Observer-based robust H∞, control for uncertain time-delay systems

2003 ◽  
Vol 44 (4) ◽  
pp. 625-634 ◽  
Author(s):  
Xinping Guan ◽  
Yichang Liu ◽  
Cailian Chen ◽  
Peng Shi
Keyword(s):  
Time Delay ◽  
Uncertain System ◽  
Delay System ◽  
Disturbance Attenuation ◽  
Delay Systems ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Parameter Uncertainties ◽  
Time Delay System ◽  
Uncertain Time

AbstractIn this paper, we present a method for the construction of a robust observer-based H∞ controller for an uncertain time-delay system. Cases of both single and multiple delays are considered. The parameter uncertainties are time-varying and norm-bounded. Observer and controller are designed to be such that the uncertain system is stable and a disturbance attenuation is guaranteed, regardless of the uncertainties. It has been shown that the above problem can be solved in terms of two linear matrix inequalities (LMIs). Finally, an illustrative example is given to show the effectiveness of the proposed techniques.

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.

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