State-space representation is a mathematical model used to describe dynamic systems. It captures the system's behavior using a set of first-order differential equations, which represent the relationships between inputs, outputs, and state variables. This approach is widely used in control theory and engineering to analyze and design systems. In state-space representation, the system is defined by matrices that represent the state dynamics, input effects, and output relationships. The state vector contains all the necessary information about the system at any given time, allowing for a comprehensive analysis of systems like electrical circuits, mechanical systems, and robotics.