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...

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...

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

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....

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...

In signal processing, a nonlinear filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals R and...

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

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

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

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

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...

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 ¨...

(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...

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

Nonlinear acoustics (NLA) is a branch of physics and acoustics dealing with sound waves of sufficiently large amplitudes. Large amplitudes require using...

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

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...

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

bifurcation theory in nonlinear dynamical systems, and he also established the theoretical frames of discontinuous dynamical systems for many applications...

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...

processing, nonlinear multidimensional signal processing (NMSP) covers all signal processing using nonlinear multidimensional signals and systems. Nonlinear multidimensional...

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...

to the linearized system, the nonlinear system has invariant manifolds, each consisting of sets of orbits of the nonlinear system. An invariant manifold...

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

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

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

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...