Controllability Criteria on Discrete-Time Impulsive Hybrid Systems With Input Delay
研究了线性离散时间脉冲混合系统在输入时滞下的可控性，通过几何和代数方法给出了零可达性、可控性及完全可控性的条件，并用算例验证了理论的有效性。
Due to the importance of the hybrid systems, the controllability for linear discrete-time impulsive hybrid systems with input delay (DIHSID) is investigated by resorting to the geometric and algebraic analytical methods in this article. First, the null reachability and controllability geometric conditions are studied. Specifically, the null reachable set and controllable set for every impulsive and switching sequence are obtained by the properties of the invariant subspace. Besides, a new subspace sequence is constructed to analyze the null reachability and controllability of DIHSID. Second, the complete controllability of DIHSID is investigated by algebraic methods. In the form of Gramian matrices, several sufficient complete controllability conditions for DIHSID are established without assuming the nonsingularity of all impulsive matrices. Furthermore, a less conservative complete controllability criterion that is necessary and sufficient is developed by introducing a row matrix of some Gramian matrices. Finally, two illustrating examples show the effectiveness of the developed controllability theory.