We live in illinois and have three children. One of the children is severely disabled. Can we exclude that child from any inheritance?

Yes, you can exclude a child.  The best way to do this is to state in your Will that you are intentionally excluding them, rather than just not listing them as a beneficiary. Another option would be to have inherited funds for your disabled child go into a Special Needs Trust.  These trusts do not disqualify individuals from receiving needs-based governmental aid but can be used to pay for extras, such as special programs or care, electronic devices, travel, eating out, etc.  A trustee, appointed by you, determines how and when any trust assets are paid on behalf of your child, and, upon your child's death, any remaining assets in the trust can go to your remaining children or grandchildren.  Organizations that work on behalf of the disabled in your state may have Special Needs Trust templates you can use.