State-space methods are mathematical frameworks used to model and analyze dynamic systems. They represent a system's state using a set of variables, allowing for the description of complex behaviors over time. This approach is widely applied in fields like control theory, signal processing, and economics. In state-space representation, systems are typically expressed in terms of state variables, input variables, and output variables. The relationships among these variables are captured through differential equations or difference equations, enabling engineers and scientists to design and predict system responses effectively.