scholarly journals Stabilization with Internal Loop for Infinite-Dimensional Discrete Time-Varying Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Nai-feng Gan ◽  
Yu-feng LU ◽  
Ting Gong
Keyword(s):  
Transfer Functions ◽  
Necessary Conditions ◽  
Time Varying ◽  
Stabilizing Controller ◽  
Infinite Dimensional ◽  
Internal Loop ◽  
Stabilizing Controllers ◽  
Time Varying Systems ◽  
Sufficient And Necessary Conditions ◽  
Well Posed

The concepts of stabilization with internal loop are analyzed for well-posed transfer functions. We obtain some sufficient and necessary conditions such that a stabilizing controller with internal loop stabilizes plant L. We also analyze two special subclasses of stabilizing controllers with internal loop, called canonical and dual canonical controllers, and show that all stabilizing controllers can be parameterized by a doubly coprime factorization of the original transfer function.

scholarly journals Stabilization of Time-Varying System by Controllers with Internal Loop

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yufeng Lu ◽  
Chengkai Shi
Keyword(s):  
Closed Loop ◽  
Time Varying ◽  
Nest Algebra ◽  
Practical Application ◽  
Closed Loop System ◽  
Infinite Dimensional ◽  
Internal Loop ◽  
Stabilizing Controllers ◽  
Strong Stabilization ◽  
Time Varying Systems

We study the concept of stabilization with internal loop for infinite-dimensional discrete time-varying systems in the framework of nest algebra. We originally give a parametrization of all stabilizing controllers with internal loop, and it covers the parametrization of canonical or dual canonical controllers with internal loop obtained before. We show that, in practical application, the controller with internal loop overcomes the awkwardness brought by the extra invertibility condition in the parametrization of the conventional controllers. We also prove that the strong stabilization problem can be completely solved in the closed-loop system with internal loop. Thus the advantage of the controller with internal loop is addressed in the framework of nest algebra.

Compensation of Time-Varying Input and State Delays for Nonlinear Systems

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Nikolaos Bekiaris-Liberis ◽  
Miroslav Krstic
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Time Varying ◽  
Feedback Systems ◽  
Feedback Controllers ◽  
Stabilizing Controller ◽  
Numerical Examples ◽  
Infinite Dimensional ◽  
State Delays ◽  
Main Challenge

We consider general nonlinear systems with time-varying input and state delays for which we design predictor-based feedback controllers. Based on a time-varying infinite-dimensional backstepping transformation that we introduce, our controller achieves global asymptotic stability in the presence of a time-varying input delay, which is proved with the aid of a strict Lyapunov function that we construct. Then, we “backstep” one time-varying integrator and we design a globally stabilizing controller for nonlinear strict-feedback systems with time-varying delays on the virtual inputs. The main challenge in this case is the construction of the backstepping transformations since the predictors for different states use different prediction windows. Our designs are illustrated by three numerical examples, including unicycle stabilization.

Model order reduction based on discrete-time Laguerre functions for discrete linear periodic time-varying systems

2020 ◽  
Vol 42 (16) ◽  
pp. 3281-3289
Author(s):  
Li-Li Sun ◽  
Kang-Li Xu ◽  
Yao-Lin Jiang
Keyword(s):  
Model Order Reduction ◽  
Transfer Functions ◽  
Order Reduction ◽  
Time Varying ◽  
Laguerre Functions ◽  
Model Order ◽  
Reduced Order ◽  
Engineering Problems ◽  
Time Varying Systems ◽  
Order Reduction Method

Many engineering problems can be modelled as linear periodic time-varying (LPTV) systems, which naturally leads to the need for model order reduction of LPTV systems. This paper investigates a new model order reduction method for discrete LPTV systems. First, the state-space realization in the Fourier-lifted form of discrete LPTV system is constructed by representing periodic matrices in exponentially modulated periodic (EMP) Fourier series. By using Laguerre functions to expand the transfer function of the resulting Fourier-lifted system, the corresponding model order reduction algorithm is developed. Furthermore, the proposed algorithm is used to reduce the discrete LPTV system in the standard-lifted form. Theoretical analysis indicates that the transfer functions of both reduced order systems can match a certain number of moments. Finally, two numerical examples are given to verify the effectiveness of the proposed method.

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