Tilstandsvariable

Tilstandsvariable (state variable) is a variable that encodes the internal state of a dynamical system at a given time and, together with the inputs, determines the system’s future behavior. The collection of all such variables forms the state vector x. In modeling, the tilstandsvariable distinguishes what must be known to predict evolution from what is external input or observed output.

In continuous-time models the evolution is described by dx/dt = f(x, u, t) and outputs by y = h(x, u, t). In discrete-time models: x_{k+1} = f(x_k, u_k, t_k), y_k = h(x_k, u_k, t_k). The specific choice of tilstandsvariable depends on the system and the level of model detail; a complete state captures all necessary information to predict future behavior, while partial or insufficient state representations require estimation.

Examples include: a pendulum described by angle and angular velocity as state; a vehicle described by position and velocity; a room thermostat modeled with temperature and heat flow as states. The state variables are the primary objects in which dynamical systems are analyzed and controlled.

Importance and applications: the concept underpins controllability and observability, which determine whether a system can be driven to a desired state and whether its state can be inferred from outputs. It is central to control methods such as state estimation (e.g., Kalman filters) and model predictive control. In computing contexts, tilstandsvariable can also refer to a program’s internal state variables that store information about execution and behavior.