Effect of Correlation on the Almost-Sure Asymptotic Stability of Second-Order Linear Stochastic Systems

1989 ◽  
Vol 56 (3) ◽  
pp. 685-690 ◽  
Author(s):  
S. T. Ariaratnam ◽  
Wei Chau Xie
Keyword(s):  
Asymptotic Stability ◽  
Gaussian Noise ◽  
Stochastic Systems ◽  
Second Order ◽  
Order Linear ◽  
Stiffness Coefficients ◽  
Special Cases ◽  
Linear Stochastic Systems ◽  
Probabilistic Property ◽  
Asymptotic Stability Condition

A method of obtaining a sufficient almost-sure (a.s.) asymptotic stability condition for second-order, linear systems with both ergodic damping and stiffness coefficients is presented. The probabilistic property of the correlation between the damping and stiffness coefficients is taken into account. A sufficient condition for a.s. asymptotic stability is derived and numerical results are presented for the case of Gaussian noise coefficients. Results obtained in some of the previous investigations are included in the present study as special cases.

Stochastic Sample Stability of Oscillatory Systems

1988 ◽  
Vol 55 (2) ◽  
pp. 458-460 ◽  
Author(s):  
S. T. Ariaratnam ◽  
W.-C. Xie
Keyword(s):  
Asymptotic Stability ◽  
Stability Condition ◽  
Gaussian Noise ◽  
Damping Coefficient ◽  
Sufficient Condition ◽  
Order Linear ◽  
Oscillatory Systems ◽  
Sample Stability ◽  
Probabilistic Property ◽  
Asymptotic Stability Condition

A method of obtaining a sufficient almost-sure asymptotic stability condition for second-order, linear oscillatory systems with an ergodic damping coefficient is presented. In this method, the probabilistic property of the derivative process of the damping coefficient is taken into account. A sufficient condition for almost-sure asymptotic stability is derived and numerical results are presented for the case of a Gaussian noise coefficient. The results are found to be an improvement over previously available results for oscillatory systems with stochastic damping.

Asymptotic Stability of Second-Order Linear Time-Varying Systems

2006 ◽  
Vol 29 (6) ◽  
pp. 1472-1476 ◽  
Author(s):  
Ryotaro Okano ◽  
Takashi Kida ◽  
Tomoyuki Nagashio
Keyword(s):  
Asymptotic Stability ◽  
Linear Time ◽  
Second Order ◽  
Time Varying ◽  
Order Linear ◽  
Time Varying Systems

Synthesis and Optimization of Transient Performances for Underdamped Second-Order Linear System Based on the Switching Control Strategy

2012 ◽  
Author(s):  
Qingyu Su ◽  
Georgi M. Dimirovski ◽  
Jun Zhao
Keyword(s):  
Linear System ◽  
Control Strategy ◽  
Optimization Problems ◽  
Switching Control ◽  
Second Order ◽  
Order Linear ◽  
Output Response ◽  
Special Cases ◽  
Switching Control Strategy ◽  
The Given

In this paper, the synthesis and optimization problems of the transient performances, such as overshoot and setting time, of the output response with respect to a step signal for an under-damped second-order linear system are studied. The traditional control strategy and the switching control strategy are used, respectively. Our control objective is twofold: Objective 1 is to ensure that the overshoot of the system output does not violate the given safety bound and objective 2 is to ensure that the settling time is smaller than the given allowable time. The obtained results indicate that the switching control strategy has main two evident advantages: firstly, the switching proportional controllers can take advantages of both the quick response and the small overshoot of the output response. Secondly, the switching controller is always available, while the single proportional controller is available in some special cases. Finally, an example of servomotor is given to demonstrate the effectiveness of the proposed method.

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