Control Theory

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12 domain-specific abstractions whose origin domain is Control Theory.

• Backstepping — A recursive nonlinear-control design method for strict-feedback systems that constructs a stabilizing controller and Lyapunov function stage by stage.
• Closed-loop transfer function — Collapse a linear feedback interconnection into the net input-to-output map—typically G(s)/(1+G(s)H(s)) for negative feedback—whose denominator exposes stability, sensitivity, and loop-gain effects.
• Controlled Invariant Subspace — A controlled invariant subspace is a linear-system state subspace whose trajectories can be kept inside it by suitable control input, equivalently one satisfying AV ⊆ V + im B or made invariant by some static state feedback.
• Dead-beat control — A discrete-time control design that drives a controllable system's state or output exactly to its target in the minimum finite number of sampling steps.
• 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.
• Kalman–Yakubovich–Popov lemma — A theorem equating a frequency-domain positivity condition for a linear system with existence of a state-space quadratic certificate.
• Optimal control — The selection of a time-dependent control policy for a dynamical system that minimizes or maximizes an objective while satisfying dynamics and constraints.
• Proper transfer function — A rational transfer function whose numerator degree does not exceed its denominator degree, so high-frequency gain remains finite.
• Rosenbrock system matrix — A polynomial block matrix combining state-space dynamics and input-output equations of a linear system.
• Separation principle — A control-theory result allowing state estimation and feedback control to be designed independently while preserving stability or optimality under stated linear-system assumptions.
• Sliding mode control — A nonlinear variable-structure control method using discontinuous feedback to drive trajectories onto a designed switching manifold and maintain reduced-order motion along it.
• State-transition matrix — A matrix function Φ(t,t₀) mapping the state of a linear dynamical system at time t₀ to its homogeneous state at time t.