换路时刻激励与系统状态跳变之间关系的进一步讨论

Further Discussion on the Relationship between the Excitation at the Switch Time and the Jump of the System State

LTI连续时间系统的系统状态在换路时刻(t=0)是否发生跳变不仅取决于系统微分方程右边形式,也取决于系统在换路时刻的激励。换路时刻激励x(t)=[x(0_+)-x(0_-)]△u(t)仅适用于阶跃信号激励情况,而不适用于单边指数信号或正余弦信号激励情况。

Whether the system state of LTI continuous-time system will jump at the switch time(t=0)depends not only on the right-hand form of the system differential equation,but also on the excitation of the system at the switch time.The excitation x(t)=[x(0+)-x(0_)]Δu(t)at the switch time is only suitable for step signal excitation,but not for single-sided exponential signal or sine-cosine signal excitation.