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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.243j (Fall 2003): DYNAMICS OF NONLINEAR SYSTEMS by A. Megretski Take-Home Test 2 1 For each problem, give an answer and provide supporting arguments, not to exceed two pages per problem. Return your test paper by 11.05 am on Wednesday November 19, in the classroom. Remember that collaboration is not allowed on test assignments. Problem T2.1 System of ODE equations x ˙( t ) = Ax ( t ) + B ( Cx ( t ) + cos ( t )) , (1.1) where A, B, C are constant matrices such that CB = 0, and : R k R q is continuously differentiable, is known to have a locally asymptotically stable non-equilibrium periodic solution x = x ( t ). What can be said about trace( A ) ? In other words, find the set of all real numbers such that = trace( A ) for some A, B, C, such that (1.1) has a locally asymptotically stable non-equilibrium periodic solution x = x ( t )....
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- Spring '09
- Dynamics, Massachusetts Institute of Technology, continuously differentiable function, Department of Electrical Engineering and Computer Science, DYNAMICS OF NONLINEAR SYSTEMS