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Observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. In control theory, the observability and controllability of a linear system are mathematical duals. The concept of observability was introduced by the Hungarian-American engineer Rudolf E. Kálmán for linear dynamic systems.
The goal is to reach any point in the plane by driving a distance in a straight line, come to a full stop, turn, and driving another distance, again, in a straight line. If your car has no steering then you can only drive straight, which means you can only drive on a line (in this case the north-south line since you started facing north).
In control theory, a state observer, state estimator, or Luenberger observer is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications.
The term is borrowed from control theory, where the "observability" of a system measures how well its state can be determined from its outputs. Similarly, software observability measures how well a system's state can be understood from the obtained telemetry (metrics, logs, traces, profiling). The definition of observability varies by vendor:
In physics, an observable is a physical property or physical quantity that can be measured.In classical mechanics, an observable is a real-valued "function" on the set of all possible system states, e.g., position and momentum.
The observability and controllability of a system are mathematical duals (i.e., as controllability provides that an input is available that brings any initial state to any desired final state, observability provides that knowing an output trajectory provides enough information to predict the initial state of the system).
has full column rank at every eigenvalue of . If, in addition, all eigenvalues of A {\displaystyle {\boldsymbol {A}}} have negative real parts ( A {\displaystyle {\boldsymbol {A}}} is stable) and the unique solution of
In control theory, we may need to find out whether or not a system such as ˙ = + () = + is controllable, where , , and are, respectively, , , and matrices for a system with inputs, state variables and outputs.