On the Stability of a Class of Distributed, Sampled-Data Nonlinear Systems

1971 ◽  
Vol 93 (3) ◽  
pp. 142-150
Author(s):  
N. Nagarajan ◽  
H. C. Khatri
Keyword(s):  
Transfer Function ◽  
Stability Criterion ◽  
Absolute Stability ◽  
Distributed Parameter ◽  
Sufficient Condition ◽  
Data Systems ◽  
Sampled Data ◽  
Nonlinear Feedback ◽  
The Stability ◽  
Domain Stability

A frequency domain stability criterion (sufficient condition) for a class of distributed parameter, sampled-data systems containing a memoryless, nonlinear feedback element is presented. This criterion for absolute stability of the class of distributed systems considered here parallels the criterion for lumped systems obtained by Jury and Lee, and it requires that the following relationship be satisfied on the unit circle (|z| = 1). Re{W(pj,z)[1+q(z−1)]}+1K−K′|q|2|(z−1)W(pj,z)|2≥0forallj=0,1,2,…. This sufficient condition is limited to those systems whose dynamics can be described by a transfer function W(pi, z) which is the ratio of the multiple transform of the output to the multiple transform of the input. An example is given to illustrate the applications of the stability criterion.

Stability Analysis of Elastic Vibration of Flexible Manipulator Arm Based on Routh Criterion

2013 ◽  
Vol 404 ◽  
pp. 182-187
Author(s):  
Yuan Chen ◽  
Guang Rui Liu ◽  
Wen Jing Wu
Keyword(s):  
Stability Analysis ◽  
Transfer Function ◽  
Stability Criterion ◽  
Elastic Vibration ◽  
Flexible Manipulator ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Manipulator Arm ◽  
The Stability ◽  
Necessary And Sufficient

dynamic model of flexible manipulator arm having end position addition mass is deduced in the first place in this paper , then the state space expression and transfer function using drive moment as input and using elastic vibration of end position as output of flexible manipulator arm are obtained . the necessary and sufficient condition assuring stability of flexible manipulator arm system is obtained using Routh criterion , and the stability criterion of the elastic motion of end position is deduced . the influence of end position addition mass and drive joint rotary inertia on the elastic motion stability of end position of manipulator arm is analyzed based on the stability criterion .

Stability Criteria for Distributed Nonlinear Sampled-Data Systems Defined by Green’s Functions

1974 ◽  
Vol 96 (3) ◽  
pp. 315-321 ◽  
Author(s):  
G. Jumarie
Keyword(s):  
Stability Criterion ◽  
Feedback Gain ◽  
Continuous Systems ◽  
Mean Square ◽  
Data Systems ◽  
Sampled Data ◽  
Input Output ◽  
Output Stability ◽  
Lumped Parameter ◽  
The Mean

Sampled-data, nonlinear, distributed systems, which exhibit a structure similar to that of the standard closed loop with lumped parameter, are investigated from the viewpoint of their input-output stability. These systems are governed by operational equations involving discrete Laplace-Green kernels. Their feedback gains are bounded by upper and lower values which depend explicitly on the time and the distributed parameter. The main result is: an input-output stability theorem is given which applies both in L∞ (O, ∞) and L2 (O, ∞). This criterion, which may be considered as being an extension of the ≪circle criterion≫, involves the mean square value on the bounds of the feedback gain. Stability conditions for continuous systems are derived from this result. In the special case of systems with distributed periodical time-varying feedback gains, a stability criterion is given which applies in Marcinkiewicz space M2 (O, ∞). This result which involves the mean square value of the feedback gain is generally less restrictive than the L2 (O, ∞) stability criterion mentioned above.

scholarly journals The Lyapunov Stability for the Linear and Nonlinear Damped Oscillator with Time-Periodic Parameters

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Jifeng Chu ◽  
Ting Xia
Keyword(s):  
Periodic Function ◽  
Lyapunov Stability ◽  
Stability Criterion ◽  
Normal Forms ◽  
Sufficient Condition ◽  
Periodic Functions ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Time Periodic ◽  
Damped Oscillator

Leta(t),b(t)be continuousT-periodic functions with∫0Tb(t)dt=0. We establish one stability criterion for the linear damped oscillatorx′′+b(t)x′+a(t)x=0. Moreover, based on the computation of the corresponding Birkhoff normal forms, we present a sufficient condition for the stability of the equilibrium of the nonlinear damped oscillatorx′′+b(t)x′+a(t)x+c(t)x2n-1+e(t,x)=0, wheren≥2,c(t)is a continuousT-periodic function,e(t,x)is continuousT-periodic intand dominated by the powerx2nin a neighborhood ofx=0.

Transfer Function Modeling of Distributed Piezoelectric Vibration Energy Harvesters

2009 ◽  
Author(s):  
Chin An Tan ◽  
Heather L. Lai
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Vibration Energy ◽  
System Response ◽  
Distributed Parameter ◽  
Domain Modeling ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Adjoint Systems ◽  
The Stability

Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.

A note on the stability of a class of sampled data systems

1972 ◽  
Vol 60 (1) ◽  
pp. 133-134
Author(s):  
J. Bertrand ◽  
T. Liakakis ◽  
E.N. Protonotarios
Keyword(s):  
Data Systems ◽  
Sampled Data ◽  
The Stability

Frequency Domain Stability Criteria for Distributed Parameter Systems

1970 ◽  
Vol 92 (2) ◽  
pp. 377-384 ◽  
Author(s):  
H. C. Khatri
Keyword(s):  
Frequency Domain ◽  
Stability Criterion ◽  
Closed Loop ◽  
Linear Time ◽  
Distributed Parameter Systems ◽  
Open Loop ◽  
Distributed Parameter ◽  
Stability Criteria ◽  
Domain Stability ◽  
Loop Stability

For distributed parameter systems, open-loop stability in the sense of bounded outputs for bounded inputs, and closed-loop asymptotic stability are considered. Frequency domain stability criteria for open and closed-loop distributed parameter systems are given. The closed-loop stability criterion is similar to V. M. Popov’s stability criterion for lumped systems. The criteria are limited to those linear, time-invariant systems whose dynamics can be described by a transfer function which is the ratio of the multiple transform of the output to the multiple transform of the input. The input may or may not be distributed. An example is given to illustrate the applications of the stability criteria.

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