A New Approach to Delay-Dependent H∞ Control of Linear State-Delayed Systems

2004 ◽  
Vol 126 (1) ◽  
pp. 201-205 ◽  
Author(s):  
De-Jin Wang
Keyword(s):  
Controller Design ◽  
Linear Matrix ◽  
State Delay ◽  
Delayed Systems ◽  
Cross Term ◽  
Closed Loop Systems ◽  
Linear State ◽  
Delay Dependent ◽  
Time Invariant ◽  
Control Criterion

An alternative delay-dependent H∞ controller design is proposed for linear, continuous, time-invariant systems with unknown state delay. The resulting delay-dependent H∞ control criterion is obtained in terms of Park’s inequality for bounding cross term. The H∞ controller determined by a convex optimization algorithm with linear matrix inequality (LMI) constraints, guarantees the asymptotic stability of the closed-loop systems and reduces the effect of the disturbance input on the controlled output to within a prescribed level. A numerical example illustrates the effectiveness of our method.

DELAYED FUZZY CONTROLLER DESIGN FOR HYPERCHAOS WITH APPLICATION TO HYPERCHAOTIC CHEN'S SYSTEM

2007 ◽  
Vol 18 (07) ◽  
pp. 1095-1105 ◽  
Author(s):  
XINGWEN LIU ◽  
XIN GAO
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed State Feedback ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Compensation Design ◽  
Hyperchaotic Systems ◽  
Control Criterion

Studied in this paper is the control problem of hyperchaotic systems. By combining Takagi–Sugeno (T–S) fuzzy model with parallel distributed compensation design technique, we propose a delay-dependent control criterion via pure delayed state feedback. Because the result is expressed in terms of linear matrix inequalities (LMIs), it is quite convenient to check in practice. Based on this criterion, a procedure is provided for designing fuzzy controller for such systems. This method is a universal one for controlling continuous hyperchaotic systems. As illustrated by its application to hyperchaotic Chen's system, the controller design is quite effective.

scholarly journals Dissipativity-Based Controller Design for Time-Delayed T-S Fuzzy Switched Distributed Parameter Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaona Song ◽  
Mi Wang ◽  
Shuai Song ◽  
Jingtao Man
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Distributed Parameter Systems ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Varying Delay ◽  
Closed Loop Systems ◽  
Control Gain

This paper studies fuzzy controller design problem for a class of nonlinear switched distributed parameter systems (DPSs) subject to time-varying delay. Initially, the original nonlinear DPSs are accurately described by Takagi-Sugeno fuzzy model in a local region. On the basis of parallel distributed compensation technique, mode-dependent fuzzy proportional and fuzzy proportional-spatial-derivative controllers are constructed, respectively. Subsequently, using single Lyapunov-Krasovskii functional and some matrix inequality methods, sufficient conditions that guarantee the stability and dissipativity of the closed-loop systems are presented in the form of linear matrix inequalities, which allow the control gain matrices to be easily obtained. Finally, numerical examples are provided to demonstrate the validity of the designed controllers.

scholarly journals Resilient Robust Finite-TimeL2-L∞Controller Design for Uncertain Neutral System with Mixed Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xia Chen ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Neutral System ◽  
Time Varying ◽  
Constraint Condition ◽  
Closed Loop System ◽  
Delayed System ◽  
Delay Dependent

The delay-dependent resilient robust finite-timeL2-L∞control problem of uncertain neutral time-delayed system is studied. The disturbance input is assumed to be energy bounded and the time delays are time-varying. Based on the Lyapunov function approach and linear matrix inequalities (LMIs) techniques, a state feedback controller is designed to guarantee that the resulted closed-loop system is finite-time bounded for all uncertainties and to satisfy a givenL2-L∞constraint condition. Simulation results illustrate the validity of the proposed approach.

scholarly journals Robust Moving HorizonH∞Control of Discrete Time-Delayed Systems with Interval Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
F. Yıldız Tascikaraoglu ◽  
I. B. Kucukdemiral ◽  
J. Imura
Keyword(s):  
Discrete Time ◽  
Disturbance Rejection ◽  
Closed Loop ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Delayed Systems ◽  
State Delays ◽  
Delay Dependent

In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.

scholarly journals Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Xie
Keyword(s):  
Controller Design ◽  
Linear Time ◽  
Admissible Solution ◽  
Linear Matrix ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Lpv Control ◽  
Lpv System ◽  
Time Invariant ◽  
Iterative Linear Matrix Inequality

A linear time-invariant (LTI) output feedback controller is designed for a linear parameter-varying (LPV) control system to achieve quadratic stability. The LPV system includes immeasurable dependent parameters that are assumed to vary in a polytopic space. To solve this control problem, a heuristic algorithm is proposed in the form of an iterative linear matrix inequality (ILMI) formulation. Furthermore, an effective method of setting an initial value of the ILMI algorithm is also proposed to increase the probability of getting an admissible solution for the controller design problem.

Delay-dependent robust H∞ control of uncertain linear state-delayed systems

Automatica ◽  
1999 ◽  
Vol 35 (7) ◽  
pp. 1313-1321 ◽  
Author(s):  
Carlos E. de Souza ◽  
Xi Li
Keyword(s):  
Delayed Systems ◽  
Linear State ◽  
Delay Dependent

Robust model predictive control synthesis for state-delayed systems with randomly occurring input saturation nonlinearities

2016 ◽  
Vol 40 (1) ◽  
pp. 179-190 ◽  
Author(s):  
Langwen Zhang ◽  
Wei Xie ◽  
Zhaozhun Zhong ◽  
Jingcheng Wang
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
State Feedback ◽  
Controller Design ◽  
Input Saturation ◽  
Time Instant ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Model Parameters ◽  
Delayed Systems

In this paper, a model predictive control algorithm is presented for linear parameter varying systems with both state delays and randomly occurring input saturation. The input saturation is assumed to be occurred randomly with Bernoulli-distributed white sequences. A constant sate feedback law is designed at each time instant to ensure the robust stability of the closed-loop system with respect to polytopic uncertainties. The optimization of model predictive controller is cast into solving a linear matrix inequalities optimization problem. Then, the results are extended to gain-scheduled approach in which a set of state feedback laws are designed for each vertex of the system model. The state feedback law is scheduled by the time varying model parameters to achieve less conservatism in controller design. Finally, two examples are employed to show the effectiveness of the proposed algorithms.

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