Sorry for the delay, I was researching IL law for you and wanted to get the correct citation for you. The law controlling your situation is as follows:
(735 ILCS 5/9-210) (from Ch. 110, par. 9-210)
Sec. 9-210. Notice to quit. When default is made in any of the terms of a lease, it is not necessary to give more than 10 days' notice to quit, or of the termination of such tenancy, and the same may be terminated on giving such notice to quit at any time after such default in any of the terms of such lease. Such notice may be substantially in the following form:
"To A.B.: You are hereby notified that in consequence of your default in (here insert the character of the default) of the premises now occupied by you, being, etc., (here describe the premises) I have elected to terminate your lease, and you are hereby notified to quit and deliver up possession of the same to me within 10 days of this date(dated, etc.)."
The notice is to be signed by the lessor or his or her agent, and no other notice or demand of possession or termination of such tenancy is necessary.
When you breached the lease agreement by having your brother's dogs for a week, that gave the landlord the legal right to terminate your lease agreement. I am sorry.
I understand that you may be disappointed by the Answer you received, as it was not particularly favorable to your situation. Had I been able to provide an Answer which might have given you a successful legal outcome, it would have been my pleasure to do so.
If you have additional questions, you may of course reply back to me and I will be happy to continue to assist you further until your questions have been answered to your satisfaction.
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Thank you in advance. I wish you the best in your future,