... catastrophic failures. 20 10 2009 02 07 2010 16 12 2010 16 12 2010 approximation theory closed loop systems discrete systems feedback linear systems nonlinear control systems nonlinear differential equations partial differential equations piezoelectric actuators plates...

... for the system. Examples are presented to illustrate the method for both continuous and hybrid systems. In this section, an existing method for directly linearizing equations of motion for discrete systems is reviewed and illustrated in a two degree of freedom example. Recall that the Lagrangian energy...

... d p = d d p { μ 1 p [ 1 − exp [ 1 − exp ( μ 2 ( 1 p − 1 ) ) ] ] } = μ 1 − μ 1 { 1 + μ 2 p exp [ μ 2 ( 1 p − 1 ) ] } exp { 1 − exp [ μ 2 ( 1 p − 1 ) ] } discrete systems...

... developed was the quantization scheme based on the Hamiltonian formulation. The presence of the constraints in the Hamiltonian formulation has specific characteristic of singular Lagrangian theories (see, for example, Ref. 44 and the references therein). discrete systems nonlinear dynamical...

... phase space methods combinatorial mathematics mesh generation computational complexity discrete systems Lyapunov methods chain recurrence Lyapunov function Conley’s decomposition theorem algorithms computation combinatorial dynamics Identifying recurrent behavior...