Analysis of non-linear non-autonomous systems by truncated point mappings

1989 ◽  
Vol 24 (4) ◽  
pp. 327-344 ◽  
Author(s):  
H. Flashner ◽  
R.S. Guttalu
Keyword(s):  
Autonomous Systems ◽  
Non Linear

A new approach to the study of non-linear non-autonomous systems

1968 ◽  
Vol 8 (1) ◽  
pp. 103-107 ◽  
Author(s):  
B.V. Dasarathy ◽  
P. Srinivasan
Keyword(s):  
Autonomous Systems ◽  
New Approach ◽  
Non Linear

Robust stabilization of non-linear non-autonomous control systems with periodic linear approximation

2020 ◽  
Author(s):  
V I Slyn’ko ◽  
Cemil Tunç ◽  
V O Bivziuk
Keyword(s):  
Autonomous Systems ◽  
Robust Stabilization ◽  
Domain Of Attraction ◽  
Linear Feedback ◽  
Partial Sums ◽  
Controlled System ◽  
Periodic Linear ◽  
Non Linear ◽  
Lyapunov Matrix ◽  
Matrix Differential

Abstract The paper deals with the problem of stabilizing the equilibrium states of a family of non-linear non-autonomous systems. It is assumed that the nominal system is a linear controlled system with periodic coefficients. For the nominal controlled system, a new method for constructing a Lyapunov function in the quadratic form with a variable matrix is proposed. This matrix is defined as an approximate solution of the Lyapunov matrix differential equation in the form of a piecewise exponential function based on partial sums of a W. Magnus series. A stabilizing control in the form of a linear feedback with a piecewise constant periodic matrix is constructed. This control simultaneously stabilizes the considered family of systems. The estimates of the domain of attraction of an asymptotically stable equilibrium state of a closed-loop system that are common for all systems are obtained. A numerical example is given.

Non-linear, non-autonomous systems of first order

Automatica ◽  
1970 ◽  
Vol 6 (6) ◽  
pp. 813-815
Author(s):  
B.V. Dasarathy
Keyword(s):  
Autonomous Systems ◽  
First Order ◽  
Non Linear

scholarly journals Existence of limit cycles for a class of autonomous systems

1983 ◽  
Vol 28 (3) ◽  
pp. 331-337
Author(s):  
Anthony Sofo
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Autonomous Systems ◽  
Non Linear ◽  
Stable Periodic ◽  
Linear Differential ◽  
Image Position

A proof is given for the existence of at least one stable periodic limit cycle solution for the polynomial non-linear differential equation of the formin some cases where the Levinson-Smith criteria are not directly applicable.

Non-linear filtering for bilinear stochastic differential systems: A Stratonovich perspective

2020 ◽  
Vol 42 (10) ◽  
pp. 1755-1768
Author(s):  
Sandhya Rathore ◽  
Shambhu N Sharma ◽  
Dhruvi Bhatt ◽  
Shaival Nagarsheth
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Dynamic Systems ◽  
Autonomous Systems ◽  
Linear Filtering ◽  
Electrical Networks ◽  
Closed Form Solutions ◽  
Dynamic Circuits ◽  
Non Linear ◽  
And Control

Bilinear stochastic differential equations have found applications to model turbulence in autonomous systems as well as switching uncertainty in non-linear dynamic circuits. In signal processing and control literature, bilinear stochastic differential equations are ubiquitous, since they capture non-linear qualitative characteristics of dynamic systems as well as offer closed-form solutions. The novelties of the paper are two: we weave bilinear filtering for the Stratonovich stochasticity. Then this paper unfolds the usefulness of bilinear filtering for switched dynamic systems. First, the Stratonovich stochasticity is embedded into a vector ‘bilinear’ time-varying stochastic differential equations. Then, coupled non-linear filtering equations are achieved. Finally, the non-linear filtering results are applied to an appealing bilinear stochastic Ćuk converter circuit. This paper also encompasses a system of coupled bilinear filtering equations for the vector input Brownian motion case. This paper brings the notions of systems theory, that is, bilinearity, Stratonovich stochasticity, non-linear filtering techniques and switched electrical networks together. Numerical simulation results are presented to demonstrate that the proposed bilinear filter can achieve much better and accurate filtering performance than the conventional Extended Kalman Filter (EKF).

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