var dataString =
            'SysSettingID=null';

        $.ajax({
            type: 'PUT',
            data: dataString,
            url: url, //funHostName() + '/api/SysSettings/' + SysSettingID + '/',
            success: function (data) {
            ...

public async Task<IHttpActionResult> PutSysSetting(int id, SysSetting sysSetting)
{
   if (!ModelState.IsValid) { ... }
}

var dataString = 'SysSettingID=' + null;
var dataString = 'SysSettingID=null';
var dataString = 'SysSettingID=' + undefined;
var dataString = 'SysSettingID=undefined';