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.

Version: v2 · 2026-09-19 · History
Domain-specific #: 4636
Domain group: Interdisciplinary & Synthetic
Origin domain: Systems Thinking & Cybernetics
Subdomain: Control Theory → Systems Thinking & Cybernetics

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.

How would you explain it like I'm…

Watch-Everything Steering

Imagine steering a toy robot by watching everything about it at once: where it is, how fast it's going, which way it's tipping. You use all of that to decide each little push. If your pushes can reach every part of how the robot moves, you get to pick how it behaves, like settling down quickly instead of wobbling.

Steering With the Whole Picture

Full state feedback is a way to control a machine by measuring every important thing about it, called its state, like position and speed. The controller multiplies each measurement by a number it picks and uses the result to adjust the push it gives. By choosing those numbers well, engineers can decide how the machine responds, such as how fast it settles and whether it wobbles. This only works if the controls can actually affect every part of the machine's motion, and if every part of the state is measured or estimated.

State-Feedback Pole Placement

In control engineering, a system can be described by a state, a list of variables capturing its current condition, and an equation for how that state changes. Full State Feedback sets the control input equal to a reference minus a gain K times the whole state. This changes the system's behavior from that of A alone to A − BK, where A describes the system and B how inputs affect it. By choosing K, engineers set the closed-loop system's eigenvalues, numbers that decide how fast and how smoothly it responds. This requires that all state variables be measured or estimated, and that the system be controllable, meaning the input can influence every behavior you want to place.

Full State Feedback applies to linear state-space models ẋ = Ax + Bu. The control law sets u = r − Kx, a reference term minus a gain matrix times the entire state vector. Substituting gives closed-loop dynamics governed by A − BK, so feedback reshapes the system matrix without changing the number of state variables. If the pair (A, B) is controllable, the eigenvalues of A − BK can be placed at arbitrary desired locations; with only partial controllability, only the controllable modes can be assigned. Gain design proceeds by matching the closed-loop characteristic polynomial, or an equivalent eigenstructure, to design targets such as speed and damping. The method assumes the full state is available, either measured directly or reconstructed by an estimator. Claiming a design is full state feedback means verifying state availability, controllability over the assigned modes, and that the chosen K actually yields the declared eigenvalues.

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.
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) — outgoing typed relations

Full state feedback is a kind of Feedback Prime

What makes it its own entry: the domain-specific identity determined by 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.

Hierarchy path (1) — routes to 1 parentless root

Full state feedback → is a kind of Feedback

Neighborhood in Abstraction Space¶

Full state feedback sits in a crowded region of the domain-specific corpus (12^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Linear Control & Circuit Systems (12 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-25