How Do I shut down a Tryndamere style splitpush strategy?

I played some matches last night and lost 3 games all to the same strategy. I need to go ahead create a strategy for beating the splitpush offense.

In the first game I lost lane to a Tryndamere as Nasus top. He would face tank my damage popping his ult to take out turrets. He got 4 man ganked and still took out an inhib before going. This was a tough one had no idea what to do.

Next game same tryndamere disconnects first 5 minutes of the game. Comes back feeds 10 kills. Still splitpushes down turrets while my team is taking objectives and trying to push. In this game Tryndamere has a Master Yi following up his splits for some serious back door threat. We lost by a hair in this one.

Last game Jayce top. I win lane as Garen. Jayce stays top and pushes while I take objectives with team. He gets to our inhib. Before we stop him. Final team fight I learn not to pick a immobile top against Kalstya Jayce back doors while his team holds us back.

Now I'm not sure what to do about these splitpushes. I warded the push next to red that splitpushers like to hide in, and we still couldn't catch these splitpushers. Is high gold just not good enough to stop a suicide splitpusher? If that's the issue I'll gladly accept the losses and implement the strategy my self.

I feel like there is something I'm missing though. Help please. This is not a Tryndamere complaint thread.