How to find backup status of databases which are online

We need to find the backup status of all database which are currently in online state . This script with not include database that is offline or in recovery state.

DECLARE @Baksql VARCHAR(8000) DECLARE @BackupFolder VARCHAR(100) DECLARE @BackupFile VARCHAR(100) DECLARE @BAK_PATH VARCHAR(4000) DEclare @BackupDate varchar(100)  
-- Setting value of  backup date and folder of the backup
SET @BackupDate =  REPLACE(REPLACE(REPLACE(CONVERT(VARCHAR,GETDATE(),120),'-',''),':',''),' ','_') -- 20110517_182551 SET @BackupFolder = 'D:\DBBackups\' SET @Baksql = ''  
-- Declaring cursor
DECLARE c_bakup CURSOR FAST_FORWARD READ_ONLY FOR   SELECT NAME FROM SYS.DATABASES  WHERE state_desc = 'ONLINE'
-- Consider databases which are online
AND database_id > 4
-- Exluding system databases    
-- Opening and fetching next values from sursor
OPEN c_bakup  FETCH NEXT FROM c_bakup INTO @BackupFile    WHILE @@FETCH_STATUS = 0 BEGIN   SET @BAK_PATH = @BackupFolder + @BackupFile  
-- Creating dynamic script for every databases backup
SET @Baksql = 'BACKUP DATABASE ['+@BackupFile+'] TO DISK = '''+@BAK_PATH+'_FullBackup_'+@BackupDate+'.bak'' WITH INIT;'  
-- Executing dynamic query
PRINT (@Baksql) EXEC(@Baksql)  
-- Opening and fetching next values from sursor
FETCH NEXT FROM c_bakup INTO @BackupFile  END  
-- Closing and Deallocating cursor
CLOSE c_bakup DEALLOCATE c_bakup