állapottérben

In physics and engineering, the concept of "állapottér" translates to "state space." State space representation is a mathematical model used to describe the behavior of dynamical systems. It utilizes a set of first-order differential or difference equations to represent the system's internal state. The state of a system is defined by a minimal set of variables, called state variables, that completely characterize its behavior at any given time.

The state space representation consists of two main equations: the state equation and the output equation. The state equation describes how the state variables evolve over time, influenced by the system's inputs. The output equation relates the system's output to its state variables and inputs. This approach is particularly useful for analyzing and designing control systems, as it provides a comprehensive view of the system's dynamics.

Unlike transfer function representations, which are typically limited to linear time-invariant (LTI) systems, state space can handle nonlinear and time-varying systems. It offers a more general framework for system analysis, enabling the study of internal states, controllability, and observability. The state space approach is widely applied in fields such as control theory, robotics, aerospace engineering, and signal processing. It allows for a more detailed understanding of system behavior, especially in complex systems where a simple input-output relationship is insufficient.