a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems...

types of nonlinear systems. Historically, system identification for nonlinear systems has developed by focusing on specific classes of system and can be...

Dynamical Systems, Caltech. Laboratory of Nonlinear Systems, Ecole Polytechnique Fédérale de Lausanne (EPFL). Center for Dynamical Systems, University...

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...

a nonlinear system is a system that is not linear—i.e., a system that does not satisfy the superposition principle. Less technically, a nonlinear system...

applies to more real-world systems because all real control systems are nonlinear. These systems are often governed by nonlinear differential equations....

In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) is called consistent if there is at least one set of values...

chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning there is...

Jacobian matrix J+ = (JTJ)−1JT instead of the inverse of J. If the nonlinear system has no solution, the method attempts to find a solution in the non-linear...

the nonlinearity. The process can be controlled with nonlinear MPC that uses a nonlinear model directly in the control application. The nonlinear model...

conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely...

nonlinear system of differential equations is the Navier–Stokes equations. Unlike the linear case, the existence of a solution of a nonlinear system is...

to the functions can be dropped if the system is unforced (i.e., it has no inputs). A classic nonlinear system is a simple unforced pendulum m ℓ 2 θ ¨...

symmetric. Linear dynamical systems can be solved exactly, in contrast to most nonlinear ones. Occasionally, a nonlinear system can be solved exactly by...

In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system. In nonlinear resonance the system behaviour – resonance frequencies...

and nonlinear systems. A linear observer structure is described in the following sections. The state of a linear, time-invariant discrete-time system is...

In signal processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs...

In time series modeling, a nonlinear autoregressive exogenous model (NARX) is a nonlinear autoregressive model which has exogenous inputs. This means that...

Stem-and-leaf displays Box plots Nonlinear analysis is often necessary when the data is recorded from a nonlinear system. Nonlinear systems can exhibit complex dynamic...

properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic...

differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the...

will just select linear terms if the system under study is linear, and nonlinear terms if the system is nonlinear, which allows a great deal of flexibility...

(link) B.H. Dayton, T.-Y. Li and Z. Zeng (2011). "Multiple zeros of nonlinear systems". Mathematics of Computation. 80 (276): 2143–2168. arXiv:2103.05738...

and Kalman filters. Nonlinear signal processing involves the analysis and processing of signals produced from nonlinear systems and can be in the time...

a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging...

nonlinear systems. In certain circumstances, which depend on the properties of the input, cross correlation between the input and output of a system with...

Flatness in systems theory is a system property that extends the notion of controllability from linear systems to nonlinear dynamical systems. A system that...

observability criteria for nonlinear time-varying systems. Observability may also be characterized for steady state systems (systems typically defined in terms...

solution for nonlinear systems. This is enabled by utilizing a homotopy-Maclaurin series to deal with the nonlinearities in the system. The HAM was first...

in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult...