tilamuuttujiin

Tilamuuttujiin is a term that appears in Finnish-language discussions of dynamic systems and state-space models. It is the illative plural form of tilamuuttuja, the Finnish word for a state variable. In modelling and control theory, tilamuuttujat are the minimal set of quantities whose values fully determine the future behavior of a system when inputs are known. The state vector, typically denoted x(t) in continuous time or x_k in discrete time, collects these variables.

In state-space representation, the evolution of tilamuuttujat is described by equations that relate the current state to its rate of change and the inputs. A common form is dx/dt = f(x, u, t) with outputs y = g(x, u, t). The tilamuuttujiin thus represent the internal condition of the system, as opposed to external inputs (u) or fixed parameters. The choice and interpretation of these variables influence model structure, estimation, and control design.

Key properties related to tilamuuttujat include observability and controllability. Observability concerns whether the current state can be inferred from measured outputs, while controllability concerns whether inputs can move the state to a desired region. The state-space approach often uses canonical forms and estimation techniques, such as Kalman filtering, to work with tilamuuttujat in practice.

Examples: in a mechanical system like a mass–spring–damper, tilamuuttujat can be position and velocity. In an electrical circuit, they might be capacitor voltage and inductor current. In each case, the tilamuuttujat provide a compact, sufficient description of the system’s present condition for predicting future behavior and designing control or estimation strategies.

See also: state-space representation, state variable, observability, controllability, Kalman filter.