scholarly journals Special issue on robust stability and control of large-scale nonlinear systems

2012 ◽  
Vol 24 (1-2) ◽  
pp. 1-2 ◽  
Author(s):  
Sergey N. Dashkovskiy ◽  
Zhong-Ping Jiang ◽  
Björn S. Rüffer
Keyword(s):  
Nonlinear Systems ◽  
Robust Stability ◽  
Large Scale ◽  
Special Issue ◽  
Stability And Control ◽  
And Control

Robust stability and control for uncertain neutral time delay systems

2012 ◽  
Vol 85 (4) ◽  
pp. 373-383 ◽  
Author(s):  
R. Sakthivel ◽  
K. Mathiyalagan ◽  
S. Marshal Anthoni
Keyword(s):  
Time Delay ◽  
Robust Stability ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Stability And Control ◽  
And Control

Hybrid Dynamical Systems: Robust Stability and Control

2006 ◽  
Author(s):  
Cai Chaohong ◽  
Goebel Rafal ◽  
G. Sanfelice Ricardo ◽  
R. Teel Andrew
Keyword(s):  
Dynamical Systems ◽  
Robust Stability ◽  
Hybrid Dynamical Systems ◽  
Stability And Control ◽  
And Control

Order Reduction of Parametrically Excited Nonlinear Systems Subjected to External Periodic Excitations

2009 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
Fundamental Solution ◽  
Invariant Manifold ◽  
Large Scale ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
And Control

In this work, some techniques for order reduction of nonlinear systems with periodic coefficients subjected to external periodic excitations are presented. The periodicity of the linear terms is assumed to be non-commensurate with the periodicity of forcing vector. The dynamical equations of motion are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the resulting equations become time-invariant while the forcing and/or nonlinearity takes the form of quasiperiodic functions. The techniques proposed here; construct a reduced order equivalent system by expressing the non-dominant states as time-varying functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states in comparison with the large scale system. Specifically, two methods are outlined to obtain the reduced order model. First approach is a straightforward application of linear method similar to the ‘Guyan reduction’, the second novel technique proposed here, utilizes the concept of ‘invariant manifolds’ for the forced problem to construct the fundamental solution. Order reduction approach based on invariant manifold technique yields unique ‘reducibility conditions’. If these ‘reducibility conditions’ are satisfied only then an accurate order reduction via ‘invariant manifold’ is possible. This approach not only yields accurate reduced order models using the fundamental solution but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover ‘resonance conditions’ associated with the fundamental solution which could be obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handing systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. These methodologies are applied to a typical problem and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems subjected to external periodic excitations.

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