How does a state vector describe the condition of a controlled system?

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In control theory, a state vector is a list of numbers that provides a quantitative summary of a system's internal dynamical state. It effectively captures the cumulative impact of all past external influences on the system up to the present moment.1

By defining the system in this way, the state vector serves as a sufficient summary to predict the future evolution of the plant, provided the future inputs are known. This allows the control action at any given time to be determined as a function of the current state, a concept known as a control law.1

Because it is often impossible to measure every component of the state vector exactly and instantaneously, modern control problems frequently involve a two-step process:
* State determination: Using an optimal filter, such as a Kalman filter, to estimate the current state vector.1
* Control application: Applying an optimal control law based on that estimate to manage the system.1