系统状态变量分析和系统时域分析的关系

本文通过把因果微分定理推广成矢量表示式,使用时域分析中的等效激励法求解状态矢量和系统输出,给出了状态变量分析中的时域计算公式的简捷推导;我们通过推导状态矢量与用0阶到n-1阶导数组成的输入输出矢量之间的关系式,用状态不跳变原理导出了输出初值跳变的计算公式,给出了冲激匹配法和等效零输入激励不变法的本质;最后,本文通过分析推导证明了状态变量分析中的时域计算公式与时域分析计算公式的一致性。

The Relationship between State Variable Analysis and Time-Domain Analysis of an LTI System

After the causal differential theorem is extended, its version in state variable analysis is given. The equivalent excitation methods in time-domain analysis of an LTI continuous system is applied to computing the state vector of the system and to further computing the system output. Thus, a more forthright and concise derivation of the time-domain computation formula in state variable analysis that is different from the derivation in the classical textbooks is put forward. By showing the formula that expresses the relationship between the state vector, input vector and output vector in which the latter two vectors are constructed by signal with corresponding differentials, the formula to compute the initial value jump of output vector is derived from the principle that state vector must continuously vary without any jump. So, the essence of impulse matching method or equivalent zero-input excitation invariable method in system time-domain analysis is given. It is proven by analysis that the time-domain computation formulae in the state variable analysis technique are totally consistent with the ones in the time-domain analysis.