对线性系统状态转移矩阵的讨论

Discussion on State Transition Matrix of Linear Systems

状态转移矩阵是现代控制理论的重要概念,在线性控制系统的运动分析中起着重要的作用。分别对连续时间线性时变系统、离散时间线性定常系统以及离散时间线性时变系统的状态转移矩阵进行了研究。根据常微分方程和差分方程解的唯一性,得到了判断矩阵函数是某一线性系统状态转移矩阵的充分条件,并求出了其对应的系统矩阵。实践证明了结论的正确性。

The state transition matrix is an important concept in modem control theory, and it plays a critical role in motion analysis for linear control systems. The state transition matrixes of continuous time linear time varying system, discrete time linear constant system, and discrete time linear time varying system are studied respectively. By using the uniqueness of solutions of ordinary differential equation and difference equation, sufficient condition for judging a matrix function to become the state transition matrix of certain linear system is obtained; and corresponding system matrixes are resolved. The practice proves that the conclusion is correct.