The Ljapunov Vector Function Method in the Analysis of Stability and other Dynamic Properties of Nonlinear Systems

1987 ◽  
pp. 57-69
Author(s):  
V. M. Matrosov
Keyword(s):  
Nonlinear Systems ◽  
Vector Function ◽  
Function Method ◽  
Dynamic Properties ◽  
Analysis Of Stability

scholarly journals The theory of nonlinear systems as an instrument for solving engineering problems

2018 ◽  
Vol 226 ◽  
pp. 04040
Author(s):  
Olga I. Ohrimenko ◽  
Igor M. Maltsev ◽  
Violetta V. Rokotyanskaya ◽  
Maria L. Vilisova
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Dynamic ◽  
Volterra Series ◽  
Dynamic Properties ◽  
Optimization Theory ◽  
Diagnostic System ◽  
Nonlinear Dynamic System ◽  
Weight Functions ◽  
Volterra Operators ◽  
Finite Set

The article outlines theoretical, methodological and practical issues of modern control and optimization theory, as well as the problems of nonlinear systems theory. Theoretical conclusions and results allowed to build mathematical models applicable to the management of objects of different nature with different principles of action, in particular, to the management of complex technical and technological objects that can be considered as nonlinear dynamic systems. The authors find it appropriate to consider nonlinear dynamic integral models as Volterra integro-power series from many functional arguments with multidimensional weight functions and a certain finite set of inputs to the system. The set of multidimensional kernels of integral Volterra operators completely characterizes the nonlinear and dynamic properties, and, consequently, the technical state of the initial system. The application of Volterra series based models allows to take into account the nonlinear and inertial properties of the initial nonlinear dynamic system more fully and accurately, it also makes the model diagnostic of a technical system more universal, raises the reliability of the forecast. The diagnostic procedure in this case is aimed at defining Volterra kernels based on the data of “input-output” experiment and building the diagnostic system of attribute in the space of which the decisive rule of optimal classification is created.

scholarly journals A filled function method for nonlinear systems of equalities and inequalities

2012 ◽  
Vol 31 (2) ◽  
pp. 391-405 ◽  
Author(s):  
Zhongping Wan ◽  
Liuyang Yuan ◽  
Jiawei Chen
Keyword(s):  
Nonlinear Systems ◽  
Function Method ◽  
Filled Function ◽  
Filled Function Method
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