There are three ways to connect a solar panel.
1) No control just hope the battery does not over charge.
2) Simple control turns excess power into heat.
3) Complex control the voltage out of the panel is altered to extract max power an inverter is used to then feed this into the battery using a step charger system.
As the size of the panel increases both the need for careful control and the benefits of careful control also increase. Clearly a 10W solar panel does not warrant a complex charging system.
Pulse Width Modulation is the buzz word read
here . The same device is used for wind chargers and solar panels.
It is normally considered over 10W you need some form of regulation. As to at what point it becomes worth using Pulse Width Modulation I am not sure. The point at which the solar panel starts putting power in the battery needs a lot less light with Pulse Width Modulation and also the power extracted from the panel is greater. So as one moves to more expensive panels the Pulse Width Modulation unit starts to pay for itself.
By time you have an inverter to lift volts to 230 and another to reduce it again to the 19 volts or what ever the laptop uses you are drawing around 10A from the battery so for one hour laptop use you need a solar panel of around 20W to replenish it. Clearly you want more than 1 hour as internal batteries will do that so looking at around 50W which are not cheap. So likely you will want a Pulse Width Modulation controller.
I looked into it all when my son lived on a boat. We decided we could buy a lot of diesel for the cost of the panels so although we fitted a 3kW inverter we did not go for the panels.
The small panels 1.5W and the like to stop battery discharging when not in use I think are a great idea. But the larger panels not so sure on. Maplin do a 40W for £80 complete with regulator that's around 2A charge with 10 hours per day average light enough for charger to work that would give around 1 hour of laptop use a day. For checking emails maybe good enough but not much else.