scholarly journals A frequency-domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential-algebraic equations (Int. J. Circ. Theor. Appl.(DOI: 10.1002/cta.440))

2009 ◽  
Vol 37 (5) ◽  
pp. 721-721
Author(s):  
F. L. Traversa ◽  
F. Bonani ◽  
S. Donati Guerrieri
Keyword(s):  
Nonlinear Systems ◽  
Frequency Domain ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Analysis Of Stability ◽  
Stability And Bifurcations ◽  
Frequency Domain Approach

CHARACTERIZATION OF DYNAMIC BIFURCATIONS IN THE FREQUENCY DOMAIN

2002 ◽  
Vol 12 (01) ◽  
pp. 87-101 ◽  
Author(s):  
GRISELDA R. ITOVICH ◽  
JORGE L. MOIOLA
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Frequency Domain ◽  
Building Blocks ◽  
Hopf Bifurcations ◽  
Frequency Domain Approach ◽  
Dynamic Bifurcations ◽  
Bifurcation Behavior

In this paper dynamical systems with certain degenerate Hopf bifurcations are considered. An analysis of the bifurcation behavior is proposed using several tools from the frequency domain approach. The analyzed bifurcations are the building blocks to understand the multiplicity of Hopf bifurcation points and to propose certain strategies in the future for controlling the bifurcation behavior in nonlinear systems.

scholarly journals On the estimation of robust stability regions for nonlinear systems with saturation

2004 ◽  
Vol 15 (3) ◽  
pp. 269-278 ◽  
Author(s):  
Daniel F. Coutinho ◽  
Daniel J. Pagano ◽  
Alexandre Trofino
Keyword(s):  
Nonlinear Systems ◽  
Robust Stability ◽  
Actuator Saturation ◽  
Quadratic Function ◽  
Differential Algebraic Equations ◽  
The State ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Algebraic Equations ◽  
Stability Regions

This paper addresses the problem of determining robust stability regions for a class of nonlinear systems with time-invariant uncertainties subject to actuator saturation. The unforced nonlinear system is represented by differential-algebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters, and the saturation nonlinearity is modelled by a sector bound condition. For this class of systems, local stability conditions in terms of linear matrix inequalities are derived based on polynomial Lyapunov functions in which the Lyapunov matrix is a quadratic function of the state and uncertain parameters. To estimate a robust stability region is considered the largest level surface of the Lyapunov function belonging to a given polytopic region of state. A numerical example is used to demonstrate the approach.

Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

<div>The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to</div><div>stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.</div>

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