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Factorization of Nonlinear Systems
1991We introduce a new concept of factor distribution for a nonlinear system as anew tool for studying the decomposition of such a system. The idea of factorizing generalizes a similar idea from linear system theory as well as the notion of controlled invariance for nonlinear systems.
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Controllability of nonlinear systems
Numerical Functional Analysis and Optimization, 1989In this paper we obtain global controllability of a semilinear system involving monotone nonlinearities of both Lipschitzian and non-Lipschitzian types.
JOSHI, MC, GEORGE, RK
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Bilinearization of Nonlinear Systems
1988In many control problems of practical interest, the cause-effect relation of a plant has to be modelled by a class of nonlinear differential equations. Because of the difficulty in dealing with general nonlinear equations, it is a normal way to linearize it regarding the operating steady state, using Taylor series expansion, and to deal with the ...
H. Schwarz +3 more
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Systems of Nonlinear Equations
1996This chapter extends chapter 2 from solving one nonlinear equation in one unknown to systems of nonlinear equations. Assume that we are given a system of n nonlinear equations for an \( n \in \mathbb{N} \) with n ≥ 2: $$ \begin{cases} f_1 (x_1 ,x_2 , \ldots ,x_n ) = 0, \hfill \\ f_2 (x_1 ,x_2 , \ldots ,x_n ) = 0, \hfill \\ \vdots \,\,\,\,\,\,\,\,\,\
Gisela Engeln-Müllges, Frank Uhlig
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Nonlinear Systems of Equations
1993In Chapter 6, we considered the problem of finding zeros (or roots) of nonlinear functions of a single variable. Now, we consider its generalization, the problem of finding the solution vectors of a system of nonlinear equations. We give a method for finding all solutions of a nonlinear system of equations f(x) = 0 for a continuously differentiable ...
Dietmar Ratz +3 more
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, 1990 Before developing the theory for systems of conservation laws, it is useful to have some specific examples in mind. In this chapter we will derive some systems of conservation laws.
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2006
Publisher Summary All the real-world systems exhibit nonlinear characteristics and do not satisfy the requirements of a linear system. The analysis of linear systems by z transform and Laplace transform is done to approximate nonlinear systems as linear ones.
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Publisher Summary All the real-world systems exhibit nonlinear characteristics and do not satisfy the requirements of a linear system. The analysis of linear systems by z transform and Laplace transform is done to approximate nonlinear systems as linear ones.
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Nonlinear Discrete Dynamical Systems
2001Most of the dynamics displayed by highly complicated nonlinear systems also appear for simple nonlinear systems. The reader is first introduced to the tent function, which is composed of two straight lines. The graphical method of iteration is introduced using this simple function since the constructions may be easily carried out with graph paper, rule,
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2014
In this chapter we investigate the dynamics of classical nonlinear Hamiltonian systems, which—a priori—are examples of continuous dynamical systems. As in the discrete case (see examples in Chap. 2), we are interested in the classification of their dynamics.
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In this chapter we investigate the dynamics of classical nonlinear Hamiltonian systems, which—a priori—are examples of continuous dynamical systems. As in the discrete case (see examples in Chap. 2), we are interested in the classification of their dynamics.
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