3 axis auto stabilized platform

Here are some other things to look at:

in the cpp file, after #include "ServoInput2.h" add:
#include <wiring.h>
#include <avr/interrupt.h>

move the declarations of the following into the cpp file and make them static as follows
static volatile unsigned int Pulses[ MAX_CHANNELS + 1]; // array holding channel pulses width value in microseconds
static volatile uint8_t Channel; // number of channels detected so far in the frame (first channel is 1)
static volatile uint8_t State; // this will be one of the following states:

remove the semicolon from the end of
uint8_t ServoInput2::getState()

at the bottom of the file, make an instance of the library for the user. There can only be one instance (there is support for only a single input capture in the arduino chip) so lets make it a little easer for the user
ServoInput2 ServoInput = ServoInput2() ;

in the header file add
#include <inttypes.h>
to the top of the header file

and add
extern ServoInput2 ServoInput; // make an instance for the user
to the bottom , just before the endif.
you will need to remove the following from the sketch
ServoInput2 servoInput(); // remove this because its declared in the source file.

I think you will need to fix some inconsistent capitalization between the sketch and the source files but these changes should get you close.