高阶系统方法 - II. 能控性与全驱性

In this paper, development in controllability of dynamical systems described by first-order state-space models is firstly overviewed briefly, and problems with the controllability theory originally introduced by Kalman are pointed out. It is then proven that a necessary and sufficient condition for a constant linear system to be controllable is that it can be equivalently expressed as a high-order fully-actuated system, and this result is also generalized, in a sense, to the case of nonlinear systems. Based on this discovery, complete-controllability of general dynamical systems is defined. Together with some other important properties, significance of super-controllability is clearly revealed as such that the system can be turned, by a feedback controller, into a high-order constant linear system with the coefficient matrices of the closed-loop eigen-polynomial being arbitrarily assignable.