State-space representation

State-space representation is a mathematical framework that describes how a system changes over time by tracking its key variables, called "states," and how those states evolve based on inputs and interactions. Think of it like keeping a scorecard of a game where you record the essential information needed to predict what happens next, then use equations to show how each piece of information updates with every step forward. This approach is powerful because it works for any type of system, from weather patterns and robots to economies and disease spread, making it one of the most useful tools in science and engineering.