A differential-algebraic condition for controllability and observability of time varying linear systems

摘要

An algebraic rank condition for controllability and observability of time-varying linear systems is given. The time-varying structure matrix is expanded in generated Lie algebra, with respect to a basis. It is proved that under a differential-algebraic condition for the time-dependent coefficients, controllability and observability are equivalent to a multivariable Kalman's condition, independent of the time-dependent terms.