Please note that in your latest update you have changed the name of the library in the build_flags. You need to use "-lalgobsec" for the compiler to look for the file libalgobsec.a.
Finally I got it to compile, thanks so much for that
In case anybody need it the final platform.ini file needs to have
If you want to have the libraries install within the project folder
I am using STM32f103C8T6 module as a arduino framework but I am unble to complile the below mentioned BMSC library in Platform IO.