Stabiloitavasta

Stabiloitavasta is a term used in Finnish control theory and related engineering disciplines to denote a system, process, or state that can be brought to and maintained at a desired stable condition through feedback control. In English-language literature the equivalent concept is stabilizable. A common formal setting is a linear time-invariant system described by x' = Ax + Bu, where x is the state vector and u is the input. The system is stabiloitavasta if there exists a feedback law u = -Kx that makes the closed-loop system x' = (A - BK)x asymptotically stable.

In continuous time, this requires that A - BK be Hurwitz (all eigenvalues have negative real parts). In discrete time, A - BK must have eigenvalues strictly inside the unit circle. Equivalently, all eigenvalues of A that are not controllable by (A,B) must be stable.

Stabiloitavasta is weaker than controllability; systems may not be fully controllable but still stabilizable if the uncontrollable modes are stable. This concept guides controller design, observer design, and robust control in domains such as aerospace, process control, and power systems.

Limitations and considerations: If any uncontrollable mode is unstable, stabilization is impossible with state feedback; disturbances, model uncertainty, and actuator constraints can affect stabilizability in practice. The term appears in Finnish technical literature and university courses dealing with dynamic systems.