scholarly journals Improved noise‐to‐state stability criteria of random nonlinear systems with stochastic impulses

2020 ◽  
Vol 15 (1) ◽  
pp. 96-109
Author(s):  
Likang Feng ◽  
Ju H. Park ◽  
Weihai Zhang
Keyword(s):  
Nonlinear Systems ◽  
Stability Criteria

Absolute Stability Criteria of Lurie-Type Nonlinear Systems With MIMO Bounded Time-Delays

2003 ◽  
Author(s):  
Shuli Guo ◽  
Shaoze Yan ◽  
Shizhu Wen
Keyword(s):  
Time Delay ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Time Delays ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Stability Criteria

The time delay of Lurie nonlinear system is systems is estimated in which the origin of the nonlinear systems is absolute stability by using a Liapunov-Razumikhn function. Many sufficient conditions are obtained about absolute stability criteria of nonlinear systems. A example is presented to explain the strange time delay phenomena.

scholarly journals Solution Bounds, Stability, and Estimation of Trapping/Stability Regions of Some Nonlinear Time-Varying Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Mark A. Pinsky ◽  
Steve Koblik
Keyword(s):  
Nonlinear Systems ◽  
Control Problems ◽  
Stability Criteria ◽  
Stability Regions ◽  
Novel Approach ◽  
Time Varying Systems ◽  
Trapping Regions ◽  
The Stability ◽  
And Control ◽  
Theoretical Results

Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science, and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which bounds the solution norms, derives the corresponding stability criteria, and estimates the trapping/stability regions for some nonautonomous and nonlinear systems, which arise in various application domains. Our inferences rest on deriving a scalar differential inequality for the norms of solutions to the initial systems. Utility of the Lipschitz inequality linearizes the associated auxiliary differential equation and yields both the upper bounds for the norms of solutions and the relevant stability criteria. To refine these inferences, we introduce a nonlinear extension of the Lipschitz inequality, which improves the developed bounds and allows estimation of the stability/trapping regions for the corresponding systems. Finally, we confirm the theoretical results in representative simulations.

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