Inducing sustained oscillations in a class of nonlinear discrete time systems

2016 ◽  
Vol 24 (6) ◽  
pp. 1162-1170 ◽  
Author(s):  
AR Hakimi ◽  
T Binazadeh
Keyword(s):  
Limit Cycle ◽  
Discrete Time ◽  
Stable Limit Cycle ◽  
Domain Of Attraction ◽  
Stable Limit ◽  
Discrete Time System ◽  
Sustained Oscillations ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems

Inducing sustained oscillations in a class of nonlinear discrete time systems is studied in this paper. The novelty of this paper is based on the proposed approach in generating stable oscillations according to limit cycle control. The limit cycle control is not formulated for nonlinear discrete time systems of any order and this paper concentrates on this issue. Considering the stable limit cycle as a positive limit set for the dynamical system, a nonlinear control law is designed to create the considered limit cycle in the phase trajectories of the closed-loop nonlinear discrete time system to achieve oscillations with the desirable amplitude and frequency. For this purpose, firstly, the limit cycle control is proposed for second-order nonlinear discrete time systems. The stability analysis of the generated limit cycle is done via a suitable Lyapunov function. Also, the domain of attraction of the created limit cycle is calculated. The proposed method is then extended for nonlinear discrete time systems of any order via the backstepping technique. Finally, computer simulations are performed for a practical example to demonstrate the ability of the designed controller in generating stable oscillations.

scholarly journals STUDYING THE STABILITY BY USING LOCAL LINEARIZATION METHOD

2020 ◽  
Vol 2 (1) ◽  
pp. 27-31
Author(s):  
Abdulghafoor Jasim Salim ◽  
Kais Ismail Ebrahem ◽  
Suhirman
Keyword(s):  
Singular Point ◽  
Limit Cycle ◽  
Autoregressive Model ◽  
Stable Limit Cycle ◽  
Linearization Method ◽  
Stable Limit ◽  
Local Linearization ◽  
Non Linear ◽  
The Stability ◽  
Local Linearization Method

Abstract: In this paper we study the stability of one of a non linear autoregressive model with trigonometric term  by using local linearization method proposed by Tuhro Ozaki .We find the singular point ,the stability of the singular point and the limit cycle. We conclude  that the proposed model under certain conditions have a non-zero singular point which is  a asymptotically salable ( when  0 ) and have an  orbitaly stable limit cycle . Also we give some examples in order to explain the method. Key Words : Non-linear Autoregressive model; Limit cycle; singular point; Stability.

Modal Control of Linear Time-Invariant Discrete-Time Systems

1969 ◽  
Vol 2 (8) ◽  
pp. T133-T136 ◽  
Author(s):  
B. Porter ◽  
T. R. Crossley
Keyword(s):  
Discrete Time ◽  
Linear Time ◽  
Feedback Loops ◽  
Modal Control ◽  
Discrete Time System ◽  
Linear Time Invariant ◽  
Modal Theory ◽  
Discrete Time Systems ◽  
Time Invariant ◽  
Time Systems

Modal control theory is applied to the design of feedback loops for linear time-invariant discrete-time systems. Modal theory is also used to demonstrate the explicit relationship which exists between the controllability of a mode of a discrete-time system and the possibility of assigning an arbitrary value to the eigenvalue of that mode.

Stability and robustness for discrete-time systems with control signal saturation

2000 ◽  
Vol 214 (1) ◽  
pp. 65-76 ◽  
Author(s):  
A R Plummer ◽  
C S Ling
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Control Signal ◽  
Design Stage ◽  
System Control ◽  
Stability Robustness ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems ◽  
Signal Saturation

All practical control systems exhibit control signal saturation. The effect that this saturation has on the control system performance, especially stability and robustness, can be significant and must be understood at the controller design stage. This paper presents conditions for global asymptotic stability and measures of stability robustness for such systems. These are demonstrated through simulation examples, and it is shown how an understanding of the stability conditions can inform the controller design process. The off-axis circle criterion is used as the basis for a sufficient condition for stability, and it is argued that this is not overly restrictive in practice. The derivations are carried out in discrete time, and servo-system control is envisaged as an important application area for the techniques; however, the results are applicable more widely.

A delay-partitioning approach to the stability analysis of discrete-time systems

Automatica ◽  
2010 ◽  
Vol 46 (3) ◽  
pp. 610-614 ◽  
Author(s):  
Xiangyu Meng ◽  
James Lam ◽  
Baozhu Du ◽  
Huijun Gao
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems ◽  
Delay Partitioning

Switching Control Design for Switched Fuzzy Discrete-Time Systems

2014 ◽  
Vol 1006-1007 ◽  
pp. 711-714
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Fuzzy Systems ◽  
Closed Loop ◽  
Control Method ◽  
Control Design ◽  
Switching Control ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems

This paper investigates the problems of stability analysis and stabilization for a class of switched fuzzy discrete-time systems. Based on a common Lyapunov functional, a switching control method has been developed for the stability analysis of switched discrete-time fuzzy systems. A new stabilization approach based on a switching parallel distributed compensation scheme is given for the closed-loop switched fuzzy systems. Finally, the illustrative example is provided to demonstrate the effectiveness of the techniques proposed in this paper.

On Self-Tuning Control of Nonminimum Phase Discrete-Time Systems Using Approximate Inverse Systems

1993 ◽  
Vol 115 (1) ◽  
pp. 12-18 ◽  
Author(s):  
Takashi Yahagi ◽  
Jianming Lu
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Output Data ◽  
Approximate Inverse ◽  
Nonminimum Phase ◽  
Discrete Time Systems ◽  
Inverse Systems ◽  
Self Tuning ◽  
The Stability ◽  
Time Systems

This paper presents a new method for self-tuning control of nonminimum phase discrete-time stochastic systems using approximate inverse systems obtained from the least-squares approximation. We show how unstable pole-zero cancellations can be avoided, and that this method has the advantage of being able to determine an approximate inverse system independently of the plant zeros. The proposed scheme uses only the available input and output data and the stability using approximate inverse systems is analyzed. Finally, the results of computer simulation are presented to show the effectiveness of the proposed method.

On stability for discrete-time non-linear singular systems with switching actuators via average dwell time approach

2016 ◽  
Vol 39 (12) ◽  
pp. 1771-1776 ◽  
Author(s):  
Yunlong Liu ◽  
Juan Wang ◽  
Cunchen Gao ◽  
Zairui Gao ◽  
Xiaojin Wu
Keyword(s):  
Discrete Time ◽  
Dwell Time ◽  
Closed Loop ◽  
Singular Systems ◽  
Average Dwell Time ◽  
Discrete Time Systems ◽  
Non Linear ◽  
The Stability ◽  
Relationship Of ◽  
Time Systems

This paper aims to study stability for discrete-time non-linear singular systems with switching actuators. A sufficient condition is addressed to ensure that non-linear closed-loop singular systems are input-to-state stable via average dwell time approach and the iterative relationship of discrete-time systems. In the stability criterion, we neither construct a certain Lyapunov function, nor design the specific structure of the control inputs. It is much easier to design each sub-controller of switching actuators via the proposed condition. Finally, a numerical example is provided to demonstrate the feasibility and effectiveness of the results obtained.

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