The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of sw...The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of aperiodic systems are presented,respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays.展开更多
The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of s...The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of periodic systems are presented, respectively.展开更多
The controllability for switched linear system with time_delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Fir...The controllability for switched linear system with time_delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time_delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis.展开更多
文摘The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of aperiodic systems are presented,respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays.
文摘The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of periodic systems are presented, respectively.
文摘The controllability for switched linear system with time_delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time_delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis.
