Remote starting/stopping Tomcat from Jenkins
If you install the manager webapp with a default set up of tomcat then it is possible to use this to install and restart applications, see 

https://tomcat.apache.org/tomcat-7.0-doc/manager-howto.html#Reload_An_Existing_Application

I feel that you are asking the wrong question however.  The problem is not how to restart Tomcat but how to be sure that it has restarted

Set a host, tomcat_port and check path then use shell code like this

while [ "$response_code" != "200" ]
do
        echo "Checking whether tomcat (${host}:${tomcat_port}/$check) is alive..."
        response_code=`curl -sL -w "%{http_code}" "http://${host}:${tomcat_port}/${check}" -o /dev/null`
        echo "Received response code $response_code"
        if [ "$response_code" != "200" ]
        then
                echo "Waiting for a bit..."
                sleep 15s
        fi;
done;
echo "Tomcat is alive!"


This will wait until the Tomcat comes back - or the containing Jenkins job will time out eventually