基于换路时刻激励模型的LTI系统时域求解

Time-domain solution of LTI systems based on excitation model at system switching-over time

为了解决在时域求因果LTI连续时间系统响应问题,通过建立系统换路时刻的激励模型并借助于冲激函数匹配法,使LTI连续时间系统各个响应的时域求解做到完善和统一。结果表明:LTI连续时间系统的全响应r(t)和零输入响应rzi(t)不仅与系统换路之前t=0_时刻的起始状态r(k)(0_)有关,还与系统在此时刻的激励信号值e(0_)有关。利用换路时刻激励模型求解LTI系统响应与拉普拉斯变换方法求解相一致。该成果解决了因果LTI连续时间系统(或常系数微分方程)的时域统一求解问题,对LTI连续时间系统响应时域求解具有实际意义。

In order to obtain a time-domain solution of causal LTI continuous-time systems, an excitation model is established at system switching-over time and the impulse function matching method is used. This brings about perfection and unity of response solution of LTI continuous-time systems on time-domain. The result shows that total response and zero-input response of LTI Continuous-Time Systems relate not only to system＇s initial status r^k^（0 ） but also to excitation signal value e（0_） at t = 0 of system switching-over time. Solution for responses of LTI Systems with the excitation model at system switching-over time is identical with that for responses of the LTI Systems with Laplace transform. This outcome solves the time-domain solution of causal LTI continuous-time systems （algebraic differential equations） and has practical significance for solving time-domain solution of LTI continuous-time systems.