state transition equation

state transition equation

[′stāt tran′zish·ən i‚kwā·zhən] (control systems) The equation satisfied by the n × n state transition matrix Φ(t, t0): ∂Φ(t, t0)/∂ t = A (t) Φ(t, t0), Φ(t0, t0) = I ; here I is the unit n × n matrix, and A (t) is the n × n matrix which appears in the vector differential equation dx (t)/ dt = A (t) x (t) for the n-component state vector x (t).