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state transition equation

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state transition equation [′stāt tran′zish·ən i‚kwā·zhən]

(control systems)

The equation satisfied by then×nstate transition matrix Φ(t,t₀): ∂Φ(t,t₀)/∂t=A(t) Φ(t,t₀), Φ(t₀,t₀) = I; hereIis the unitn×nmatrix, andA(t) is then×nmatrix which appears in the vector differential equationdx(t)/dt=A(t)x(t) for then-component state vectorx(t).

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