New to FSM, can someone explain how the flow works? If I use a case scenario in a loop, how is an external change detected and brought back to the loop? Is all of the code/inputs, etc to be included within the case statements?

Still having a few problems. I have modified my code to include some of the suggestions. You can see that I added some print statements to allow me to monitor execution, but I can't get it to obey, such as print "trigger" when the PIR sensor is HIGH. Anyone available to explain my error(s)? I added a void check() just to bypass the keypad (not connected).

//////////////////////////// Initialize & Includes //////////////////////////
#include "SIM900.h"
#include "sms.h"
#include "Keypad.h"
#include <GSM.h>
SMSGSM sms;
//To change pins for Software Serial, use the two lines in GSM.cpp.
int PIR_SensorPin = 2;
int LED_OutPin = 11; //green
int Alarm_OutPin = 12; //red
int alarm_count = 0;
int switchPIN = 3; // alarm on test
char keypadPIN;
int z = 0;
int i = 0;
int waitTime = 5000;

//////////////////////////// Setup Keypad //////////////////////////
const byte ROWS = 4; //four rows
const byte COLS = 4; //four columns
char keys[ROWS][COLS] =
{
  {
    '1', '2', '3', 'A'
  }
  ,
  {
    '4', '5', '6', 'B'
  }
  ,
  {
    '7', '8', '9', 'C'
  }
  ,
  {
    '*', '0', '#', 'D'
  }
};
byte rowPins[ROWS] = {
  6, 7, A2, A3 // row pin# on keypad to Arduino pin#, ie Row Pin #1 goes to Arduino Pin #6, etc.
}; // connect to the row pinouts of the keypad
byte colPins[COLS] = {
  3, A0, A1, A4
}; // connect to the column pinouts of the keypad
Keypad keypad = Keypad(makeKeymap(keys), rowPins, colPins, ROWS, COLS );
const char PIN[5] = {
  '9', '6', '7', '9', '#'
}; // PIN number
char key_input[5] = {
  0, 0, 0, 0, 0
}; // used for comparison

//////////////////////////////// Setup ///////////////////////////////////
void setup() {
  Serial.begin (9600);  // Establish Serial connection;
  pinMode (LED_OutPin, OUTPUT);     // Set pinMode.
  pinMode (Alarm_OutPin, OUTPUT);   // Set pinMode.
  pinMode (PIR_SensorPin, INPUT);   // Set pinMode.
  digitalWrite (LED_OutPin, LOW);   // Set output pins to LOW for start.
  digitalWrite (Alarm_OutPin, LOW); // Set output pins to LOW for start.
  digitalWrite (PIR_SensorPin, LOW);
  Serial.println ("Studio Alarm starting up."); // Serial message that GSM shield is starting up
  if (gsm.begin(4800)) {    // Set GSM shield to recommended 4800 baud rate.
    Serial.println ("Status = Network READY");
    digitalWrite (LED_OutPin, HIGH);
  }
  attachInterrupt (digitalPinToInterrupt (2), trigger, CHANGE); // PIR as interrupt
  // Could make use of the interrupts by checking in the interrupt if the state is "Ready" and
  // then setting the state to "Alarm".
  Serial.println ("System Ready");

  keypadPIN = HIGH;
}

//////////////////////////// State Setup //////////////////////////
enum STATE {
  Ready, //system acknowledges trigger
  Unarmed, //system unarmed via keypad entry setting keypadPIN = LOW
  JustActivated, //PIR-triggered interrupt
  Alarm // confirm system unarmed then goto unarmed state else start alarm
};
STATE systemState = Unarmed;
long timeGettingArmed;

/////////////////////////// Trigger ///////////////////////////////
void trigger() {
  systemState = JustActivated;
}

//////////////////////////// State Machine //////////////////////////
void loop() {
  check ();
  switch (systemState) {Serial.println("switch");
    case Ready:
      if (PIR_SensorPin == HIGH) {Serial.println("PIR_Sensor");
        Serial.println("triggered");
        systemState = Alarm;
      } else if (keypadPIN == LOW) {
        systemState = Unarmed;
      }
      break;
    case Unarmed:
      if (keypadPIN == HIGH) {Serial.println("keypadPIN=HIGH");
        // Serial.println("Unarmed");
        timeGettingArmed = millis();Serial.println(timeGettingArmed);
         systemState = JustActivated;
      }
      break;
    case JustActivated:Serial.println("JustActivated");
      if (timeGettingArmed + waitTime < millis()) {
        Serial.println("Ready");
        systemState = Ready;
      }
      break;
    case Alarm:
      if (keypadPIN == LOW) {Serial.println("keypadPIN=LOW");
        systemState = Unarmed;
      } else {
        beep();
      }
      break;
  }
}

//////////////////////////// Alarm //////////////////////////
void beep() {
  Serial.println("at beep");
  // (sms.SendSMS("8656171435", "*** Motion Detected in Studio! ***"));
  Serial.println ("MOTION detected: SMS Sent");
  for (alarm_count = 0; alarm_count <= 5; alarm_count++) { // Cycle outputs if triggered
    digitalWrite (Alarm_OutPin, HIGH); delay (1000); // On/Off/On/Off/Off
    digitalWrite (Alarm_OutPin, LOW); delay (500);
    digitalWrite (LED_OutPin, HIGH); // delay (1000);
    Serial.println (alarm_count);
  }
  systemState = Ready;
}

void check() {
  if (switchPIN == HIGH) { 
    keypadPIN = LOW; // Unarmed
  }
  else {
    keypadPIN = HIGH; // Ready/Armed
  }
}