Concept:
Different Indian philosophical systems define Yoga from their own perspectives. The Vaisheshika philosophy considers Yoga as a state in which suffering ceases due to stability and balance of the body, mind, and soul.
This interpretation emphasizes harmony and freedom from pain through disciplined living and mental steadiness.
Step 1: Understand the meaning of the given definition of Yoga.
The statement:
\[
\text{``Yoga is lack of suffering due to the stability of body, mind and soul.''}
\]
describes Yoga as a condition of inner equilibrium where disturbances and suffering disappear.
This idea is associated with:
\[
\text{Vaisheshika Philosophy}
\]
Step 2: Analyze the given options.
Option (A): Vaisheshika
Correct. Vaisheshika philosophy gives this interpretation of Yoga emphasizing freedom from suffering through stability.
Option (B): Shiv Samhita
Shiv Samhita mainly discusses Hatha Yoga, Kundalini, Mudras, and spiritual practices.
Option (C): Maharishi Vashishtha
Maharishi Vashishtha is associated with spiritual teachings and Yoga Vashishtha but not specifically this definition.
Option (D): Kathopnishada
Kathopanishad discusses self-realization and control of senses but not this exact definition.
Step 3: Identify the correct option.
Since this definition of Yoga is associated with Vaisheshika philosophy, the correct answer is:
\[
\boxed{\text{Vaisheshika}}
\]