# Category: Nonlinear control

Lyapunov redesign
In nonlinear control, the technique of Lyapunov redesign refers to the design where a stabilizing state feedback controller can be constructed with knowledge of the Lyapunov function . Consider the sy
Popov criterion
In nonlinear control and stability theory, the Popov criterion is a stability criterion by Vasile M. Popov for the absolute stability of a class of nonlinear systems whose nonlinearity must satisfy an
Backstepping
In control theory, backstepping is a technique developed circa 1990 by Petar V. Kokotovic and others for designing stabilizing controls for a special class of nonlinear dynamical systems. These system
Singular perturbation
In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero. More precisely, the solution cannot be uni
Feedback linearization
Feedback linearization is a common strategy employed in nonlinear control to control nonlinear systems. Feedback linearization techniques may be applied to nonlinear control systems of the form where
Phase plane
In applied mathematics, in particular the context of nonlinear system analysis, a phase plane is a visual display of certain characteristics of certain kinds of differential equations; a coordinate pl
Small-gain theorem
In nonlinear systems, the formalism of input-output stability is an important tool in studying the stability of interconnected systems since the gain of a system directly relates to how the norm of a
Variable structure control
Variable structure control (VSC) is a form of discontinuous nonlinear control. The method alters the dynamics of a nonlinear system by application of a high-frequency switching control. The state-feed
Gain scheduling
In control theory, gain scheduling is an approach to control of non-linear systems that uses a family of linear controllers, each of which provides satisfactory control for a different operating point
Variable structure system
A variable structure system, or VSS, is a discontinuous nonlinear system of the form where is the state vector, is the time variable, and is a piecewise continuous function. Due to the piecewise conti
Circle criterion
In nonlinear control and stability theory, the circle criterion is a stability criterion for nonlinear time-varying systems. It can be viewed as a generalization of the Nyquist stability criterion for
Kalman's conjecture
Kalman's conjecture or Kalman problem is a disproved conjecture on absolute stability of nonlinear control system with one scalar nonlinearity, which belongs to the sector of linear stability. Kalman'
Nonlinear control
Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics
Small control property
For applied mathematics, in nonlinear control theory, a non-linear system of the form is said to satisfy the small control property if for every there exists a so that for all there exists a so that t
Describing function
In control systems theory, the describing function (DF) method, developed by Nikolay Mitrofanovich Krylov and Nikolay Bogoliubov in the 1930s, and extended by Ralph Kochenburger is an approximate proc
Strict-feedback form
In control theory, dynamical systems are in strict-feedback form when they can be expressed as where * with , * are scalars, * is a scalar input to the system, * vanish at the origin (i.e., ), *
Sliding mode control
In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued
Aizerman's conjecture
In nonlinear control, Aizerman's conjecture or Aizerman problem states that a linear system in feedback with a sector nonlinearity would be stable if the linear system is stable for any linear gain of
Input-to-state stability
Input-to-state stability (ISS) is a stability notion widely used to study stability of nonlinear control systems with external inputs. Roughly speaking, a control system is ISS if it is globally asymp