Eigenstructure-based analysis for non-linear autonomous systems

2013 ◽  
Vol 32 (1) ◽  
pp. 21-40 ◽  
Author(s):  
H. Ghane ◽  
M. B. Menhaj
1968 ◽  
Vol 8 (1) ◽  
pp. 103-107 ◽  
Author(s):  
B.V. Dasarathy ◽  
P. Srinivasan

Author(s):  
V I Slyn’ko ◽  
Cemil Tunç ◽  
V O Bivziuk

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.


Automatica ◽  
1970 ◽  
Vol 6 (6) ◽  
pp. 813-815
Author(s):  
B.V. Dasarathy

1983 ◽  
Vol 28 (3) ◽  
pp. 331-337
Author(s):  
Anthony Sofo

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.


2020 ◽  
Vol 42 (10) ◽  
pp. 1755-1768
Author(s):  
Sandhya Rathore ◽  
Shambhu N Sharma ◽  
Dhruvi Bhatt ◽  
Shaival Nagarsheth

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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