using mingw gcc to compile under Cygwin

I want to use the mat file API to read mat files into some existing C code that runs under Cygwin, but I can't compile the example code supplied with my Matlab distribution. I am trying to compile matdgns.c to run under Cygwin. I can compile the code under Linux on another machine, and I can compile matdgns.c to run from the Windows 10 command prompt using mex and the Mingw gcc compiler. I tried using the same gcc command (modifying the paths, of course) that I used on Linux and Windows, but I get the following error when I try to do that:

matdgns.c:24:17: fatal error: mat.h: No such file or directory compilation terminated.

I've checked, and mat.h exists in the library location I am pointing to.

Here is my gcc command:

/cygdrive/c/TDM-GCC-64/bin/gcc -c -DTARGET_API_VERSION=700  -DUSE_MEX_CMD   -m64  -I"/cygdrive/c/MATLAB/R2017a/extern/include" -I"/cygdrive/c/MATLAB/R2017a/simulink/include" -I"/cygdrive/c/MATLAB/R2017a/extern/lib/win64/mingw64" -fexceptions -fno-omit-frame-pointer -O -DNDEBUG matdgns.c -o matdgns.obj

I'm running R2017a, but have tried this under R2016a, with similar results. Is it possible to do what I'm attempting? How can I successfully compile?