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 relate the system's inputs, outputs, and internal states. This approach is widely used in control theory and engineering to analyze and design systems. In state-space representation, the system is defined by state variables that represent its current condition. These variables are organized into a state vector, while the system's dynamics are expressed through matrices. This framework allows for a comprehensive analysis of both linear and nonlinear systems, making it a powerful tool in fields like control engineering and robotics.