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Statement of a problem № m52585

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A linear dynamical system can be represented by the equations Dx / dt = A(t)x(t) + B(t)u(t), y(t) = C(t)x(t) + D(t)u(t), where A is an n × n variable matrix, B is an n × r variable matrix, C is an m × n variable matrix, D is an m × r variable matrix, x is an n-dimensional vector variable, y is an m-dimensional vector variable, and u is an r-dimensional vector variable. For the system to be stable, the matrix A must have all its eigenvalues with nonpositive real part for all t. Is the system stable if a. b.




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