Full state feedback¶
A control design that feeds a measured or estimated state vector through a gain matrix to place a controllable linear system’s closed-loop poles.
Core Idea¶
For a linear state model, the input is chosen as a reference term minus K times the state so the closed-loop state matrix becomes A minus BK; controllability permits assignment of its eigenvalues. State feedback changes the system matrix without changing the plant state dimension, and gain selection matches the closed-loop characteristic polynomial or equivalent eigenstructure to design targets. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Full state feedback belongs to control theory and is useful where the analyst can specify the typed control theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the full state is available or estimated, the plant pair is controllable over the assigned modes, and the chosen gain gives the declared closed-loop eigenvalues. The scope is broad within that domain but bounded by the need for the full state is available or estimated, the plant pair is controllable over the assigned modes, and the chosen gain gives the declared closed-loop eigenvalues. Conceptual linear-control identity only; no vehicle, aircraft, weapon, industrial-plant, or hazardous-system tuning instructions are provided.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the full state is available or estimated, the plant pair is controllable over the assigned modes, and the chosen gain gives the declared closed-loop eigenvalues the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Full state feedback can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Full state feedback. Full state feedback compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed control theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the full state is available or estimated, the plant pair is controllable over the assigned modes, and the chosen gain gives the declared closed-loop eigenvalues independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of control theory because they reuse the typed control theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, State feedback changes the system matrix without changing the plant state dimension, and gain selection matches the closed-loop characteristic polynomial or equivalent eigenstructure to design targets., and type the carrier, state every parameter and convention in the definition, test that the full state is available or estimated, the plant pair is controllable over the assigned modes, and the chosen gain gives the declared closed-loop eigenvalues, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Full state feedback Domain-specific
Parents (1) — more general patterns this builds on
-
Full state feedback is a kind of Feedback Prime
The proposed strict upward parent is
prime:feedback.
Hierarchy path (1) — routes to 1 parentless root
- Full state feedback → Feedback
Neighborhood in Abstraction Space¶
Full state feedback sits in a crowded region of the domain-specific corpus (22nd percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Feedback Control & Dynamical Systems (29 abstractions)
Nearest neighbors
- Separation principle — 0.93
- Backstepping — 0.91
- Proper transfer function — 0.91
- System identification — 0.91
- Rosenbrock system matrix — 0.91
Computed from structural-signature embeddings · 2026-09-08