Having said all of that, anger and irritability - especially in men - can be a sign of depression. To put it another way, when someone's angry a lot of the time it can be a sign that they're actually really unhappy.
As you say, you don't know what's going on with him - I assume because he's not telling you what it is that he's actually struggling with it. He may not even know himself.
What we commonly think of as depression - being quiet, feeling despondent, sad or even numb, hopeless and having less sense of the future can be thought of as a turning inwards - a form of self-attack.
Anger in the way you're describing it is a form of outward attack - of putting the unhappiness on the outside and then attacking it. What we more commonly think of as "taking it out on others".
The natural response, and even a necessary response especially if this anger is spilling out around your kids, is to try and set limits - to make it clear that the behaviour is not okay. And if you're already doing that then you should probably keep doing that. At the same time, if we just do this then the real reasons behind the unhappiness don't get addressed.
It can just escalate into a fight about anger and whether it's justified. Which tends to not get very far because anger always feels justified. It's part of what anger makes us think - that we're right.
So as well as doing that, I'd encourage you to make space to try and talk about what's going on. Wait for a relatively calm moment - a strategy known as "striking when the iron's cold" - and gently say you're worried about him, and that you've noticed a change in him.
Let him know you want to know what's going on and that you'd prefer to hear about it rather than have it taken out on you. If he can't, or won't do that, let him know that he may want to consider that his anger is actually a sign something else is going on, and he may want to talk to the family GP, or a counsellor - and offer to go with him.
Because when we can move from acting on our feelings - through anger in this instance - to talking about our feelings then they get lighter and problems, along with solutions get clearer.
In this sense, it's not anger management that's needed, it's all of our emotions that need managing - and ideally expressing, with words.