Memoryless Adaptive Controller Design for Uncertain Polynomial Systems With Multiple Time Delays

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Chang-Chun Hua ◽  
Qing-Guo Wang ◽  
Peng Shi ◽  
Xin-Ping Guan
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Adaptive Controller ◽  
Polynomial Systems ◽  
Multiple Time ◽  
Control Input ◽  
Closed Loop System ◽  
Polynomial Type ◽  
Exponentially Stable ◽  
Delay Dependent

The stabilization problem is investigated for a class of uncertain systems with multiple time-varying delays. The considered system includes the uncertain nonlinear time delay functions, whose bounds are in the form of polynomial-type functions with unknown coefficients. The system is decomposed into two subsystems based on the input matrix. For the first subsystem, a time delay dependent linear virtual control input is constructed. Then, a memoryless state feedback controller is designed based on backstepping method. By employing new Lyapunov–Krasovskii functional, we show that the closed-loop system is exponentially stable. Finally, simulations are conducted to verify the effectiveness of the proposed method.

Robust Stability Analysis of Delay-Dependence for a Class of Switched Uncertain Systems with Time Delay

2013 ◽  
Vol 415 ◽  
pp. 139-142
Author(s):  
Chi Jo Wang ◽  
Juing Shian Chiou
Keyword(s):  
Time Delay ◽  
Stability Margin ◽  
Uncertain System ◽  
Switching Law ◽  
Delay Dependence ◽  
Robust Stability Analysis ◽  
Exponentially Stable ◽  
Delay Dependent ◽  
Interval Systems ◽  
Delay Dependent Stability

Some new criteria of delay-dependent stability for the switched time-delay uncertain system are deduced by employing time-switched method and the comparison theorem in this paper. The total activation time ratio of the switching law can be determined to guarantee the switched time-delay uncertain system is exponentially stable with stability margin . Finally, this method can be extended to switched interval systems with time-delay. Some examples are exploited to illustrate the proposed schemes..

Backstepping Based Adaptive Control of Magnetic Levitation System

2013 ◽  
Vol 341-342 ◽  
pp. 945-948 ◽  
Author(s):  
Wei Zhou ◽  
Bao Bin Liu
Keyword(s):  
Parameter Uncertainty ◽  
Closed Loop ◽  
Controller Design ◽  
Magnetic Levitation ◽  
Adaptive Controller ◽  
Closed Loop System ◽  
Actual System ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Control Accuracy

In view of parameter uncertainty in the magnetic levitation system, the adaptive controller design problem is investigated for the system. Nonlinear adaptive controller based on backstepping is proposed for the design of the actual system with parameter uncertainty. The controller can estimate the uncertainty parameter online so as to improve control accuracy. Theoretical analysis shows that the closed-loop system is stable regardless of parameter uncertainty. Simulation results demonstrate the effectiveness of the presented method.

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 H∞Control for Flexible Spacecraft with Time-Varying Input Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ran Zhang ◽  
Tao Li ◽  
Lei Guo
Keyword(s):  
Design Method ◽  
Flexible Spacecraft ◽  
Input Delay ◽  
Control Input ◽  
Time Varying ◽  
Closed Loop System ◽  
Slack Variables ◽  
Attenuation Level ◽  
Delay Dependent ◽  
Dependent State

This paper is concerned withH∞control problem for flexible spacecraft with disturbance and time-varying control input delay. By constructing an augmented Lyapunov functional with slack variables, a new delay-dependent state feedback controller is obtained in terms of linear inequality matrix. These slack variables can make the design more flexible, and the resultant design also can guarantee the asymptotic stability andH∞attenuation level of closed-loop system. The effectiveness of the proposed design method is illustrated via a numerical example.

A New Controller of Stochastic Delay Systems

2011 ◽  
Vol 63-64 ◽  
pp. 974-977
Author(s):  
Yun Chen ◽  
Qing Qing Li
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Stochastic Systems ◽  
Delay Systems ◽  
Mean Square ◽  
Closed Loop System ◽  
Stochastic Delay ◽  
Numerical Example ◽  
Mean Square Stability ◽  
Delay Dependent

By introducing an additional vector, a new delay-dependent controller is designed for stochastic systems with time delay in this paper. The presented controller is formulated by means of LMI, and it guarantees robust asymptotical mean-square stability of the resulting closed-loop system. Our result shows advantage over some existing ones, which is demonstrated by a numerical example.

Delay-Dependent Exponential Stabilization for Linear Distributed Parameter Systems With Time-Varying Delay

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Jun-Wei Wang ◽  
Chang-Yin Sun
Keyword(s):  
Time Delay ◽  
Distributed Parameter Systems ◽  
Dirichlet Boundary Conditions ◽  
Exponential Stabilization ◽  
Distributed Parameter ◽  
Control Input ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

This paper extends the framework of Lyapunov–Krasovskii functional to address the problem of exponential stabilization for a class of linearly distributed parameter systems (DPSs) with continuous differentiable time-varying delay and a spatiotemporal control input, where the system model is described by parabolic partial differential-difference equations (PDdEs) subject to homogeneous Neumann or Dirichlet boundary conditions. By constructing an appropriate Lyapunov–Krasovskii functional candidate and using some inequality techniques (e.g., spatial integral form of Jensen's inequalities and vector-valued Wirtinger's inequalities), some delay-dependent exponential stabilization conditions are derived, and presented in terms of standard linear matrix inequalities (LMIs). These stabilization conditions are applicable to both slow-varying and fast-varying time delay cases. The detailed and rigorous proof of the closed-loop exponential stability is also provided in this paper. Moreover, the main results of this paper are reduced to the constant time delay case and extended to the stochastic time-varying delay case, and also extended to address the problem of exponential stabilization for linear parabolic PDdE systems with a temporal control input. The numerical simulation results of two examples show the effectiveness and merit of the main results.

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