Is my divorce valid if we signed a handwritten paper with no witnesses?

Due to problems in my marriage my husband at times was not providing for me or my kids or practising Islam. I decided to ask for divorce after many attempts to fix my marriage. I wrote on paper to him saying "I divorce you" three times. He signed it and I signed it. He didn't say it and he says at times he felt pressured and didn't want to give it me. There were no witnesses at the time of signing the letter. It was hand written not, an official one. That was nearly 6 years ago. He since has married again but he says he has been told that our nikkah is still valid. He still wants me as his wife and wants to reconcile. I don't believe we are still married. I haven't remarried and have been on my own since our spilt. Is the divorce valid?