Constructing a Lyapunov function that produces the best estimator in absolute stability problems

1992 ◽  
Vol 60 (3) ◽  
pp. 1525-1528
Author(s):  
A. G. Zhuikova ◽  
D. Ya. Khusainov
Keyword(s):  
Lyapunov Function ◽  
Absolute Stability ◽  
Stability Problems ◽  
Best Estimator

Absolute Stability of a Class of Singular Nonlinear Systems with Set-Valued Mappings

2014 ◽  
Vol 24 (01) ◽  
pp. 1550015 ◽  
Author(s):  
Gaoming Feng ◽  
Xingguo Tan
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Absolute Stability ◽  
Delay Systems ◽  
Stability Conditions ◽  
Time Delay Systems ◽  
Set Valued Mappings ◽  
The Absolute

A class of singular nonlinear systems with set-valued mappings are studied in this paper. Criteria are given based on the Lyapunov function to check the absolute stability of the systems, then the results are extended to the time delay systems and the time delay systems with uncertainty. Three examples are simulated to show the effectiveness of the proposed stability conditions.

scholarly journals ABSOLUTE STABILITY OF A PROGRAM MANIFOLD OF NON-AUTONOMOUS BASIC CONTROL SYSTEMS

2018 ◽  
pp. 37-43
Author(s):  
Sailaubay Zhumatov
Keyword(s):  
Inverse Problem ◽  
Lyapunov Function ◽  
Control Systems ◽  
Absolute Stability ◽  
High Speed ◽  
Inverse Dynamics ◽  
Sufficient Conditions ◽  
System Of Differential Equations ◽  
Inverse Problems Of Dynamics ◽  
The Stability

In this paper the inverse dynamics problemisstudied: for a given manifold restore a force field, which lies in the tangent subspace to manifold. One of the general inverse problems of dynamics is solved: the corresponding system of differential equations is but as well as the stability is considered. This inverse problem is very important for a variety of mathematical models mechanics.Absolutestability of a program manifold of nonautonomous basic control systems with stationary nonlinearity is investigated.Theproblem of stability of the basic control systems is considered in the neighborhood of a program manifold. Nonlinearitysatisfies to conditions of local quadratic relations. The sufficient conditions of the absolute stability of the program manifold have been obtained relatively to a given vector-function by means of construction of Lyapunov function, in the form "quadratic form plus an integral from nonlinearity". The obtained results are used to solve the problem of the synthesis of high-speed regulators.

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