tillståndsrummodell

A tillståndsrummodell, often translated as state-space model, is a mathematical framework used to describe the behavior of a system. It represents the system's internal condition through a set of variables called state variables. These variables capture the essential information about the system at any given time, and their evolution over time dictates the system's future behavior.

The model typically consists of two main equations. The state equation describes how the state variables change with respect to time, influenced by the system's inputs and its current state. The output equation relates the system's observable outputs to its current state and inputs. This representation is particularly useful for dynamic systems, where changes occur over time.

Tillståndsrummodeller are widely used in various fields, including control engineering, signal processing, economics, and robotics. They provide a systematic way to analyze system stability, design controllers, and predict system responses to different inputs. The state-space approach offers a powerful and flexible tool for understanding and manipulating complex systems compared to traditional input-output models. The concept allows for a clear separation of internal dynamics from external observations.