Is it permissible to commission another to perform hajj on my behalf due to my illness?

'Abdullah Ibn Abbas (may God be pleased with them both) said, "Al-Fadl Ibn Abbas was riding behind the Messenger of God when a woman from Khath'am approached the Prophet and asked, 'O Messenger of God! My father is an old man; he is unable to ride to hajj and therefore cannot fulfill this obligation. Is it permissible for me to perform hajj on his behalf?' ‘Yes,’ the Prophet replied (Bukhari and Muslim).

A person who is unable to use any means of transportation due to a chronic illness or old age is called 'ma'dub'. Based on this, it is permissible to commission another to perform hajj on your behalf.

Conditions for the permissibility of commissioning another to perform hajj on one's behalf
- That the expenses of the journey be from the money of the commissioner (who is unable to perform the journey himself), from the money of the deceased (if he had asked that someone perform hajj on his behalf after his death, or from donated money if the deceased had not asked that hajj be performed on his behalf).
- That the agent make the intention to perform hajj on behalf of the person who is unable to go himself or on behalf of the deceased.
- That the commissioned person had made his own obligatory hajj.

And God Almighty knows best.