Dear Mr. Raja
There is no specific provision under the Companies Act, 1956, with respect to Special Invitees. Any person who is calling a Board Meeting or issuing a Notice of the Board Meeting i.e. either Company Secretary or Director, can call the Special Invitee at the instruction of the Chairman or Managing Director or Whole-time Director, in whose direction the Board Meeting is called for, to attend a Board Meeting for a particular item of the Board Meeting or for whole of the Meeting.
This is as per the discretion of the Chairman of the Meeting. But, before the meeting, kindly brief the Special Invitee that he is called either for whole Board Meeting or for a particular specific item, so that, he / she should not feel awkward, when asked to leave the Board Meeting in-between.
I hope that I have clarified the situation. Still you need any other assistance, feel free to contact me.