线性时变广义系统的能控性与能观性问题

On Controllability and Observability of Linear Time-varying Singular Systems

讨论了线性时变系统和线性时变广义系统的两个基本问题,得到了两种判定时变系统能控性与能观性的必要条件,该判定条件只依赖于系统矩阵A(t)和输入矩阵B(t),不必计算系统的系统状态转移矩阵,使得判别时变系统能控性与能观性易于实现.说明了本文结论是线性定常系统相应结论的自然扩展.对进一步深入研究时变系统和时变广义系统具有实际启发作用.

Two basic issues of time-varying systems and timevarying singular systems are discussed. Two necessary conditions to judge the controllability and observability of timevarying systems and time-varying singular systems are obtained. The conditions only depend on the system matrix and input matrix, without introducing and calculating system state transition matrix. It is easy to judge the controllability and observability of time-varying systems and time-varying singular systems. The result extends the corresponding conclusion of linear time invariant systems. The paper may practically enlighten the research on time-varying systems.