Introduction
In this book we have presented a theory which provides a general approach to nonlinear problems in systems theory. The method consists of writing a nonlinear system as the limit of a sequence of an approximating sequence of linear, time-varying ones and applying linear theory to each of the approximating systems. We have proved general convergence theorems and given applications to frequency-domain theory of nonlinear systems, optimal control, nonlinear sliding control and to nonlinear partial differential equations.
In this final chapter we shall show that there are many more potential applications of the method by using two illustrative examples which are now in the process of development. One is the application of the method to the problem of travelling waves in nonlinear partial differential equations and the other is to the separation theorem for nonlinear stochastic systems.
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Tomás-Rodríguez, M., Banks, S.P. (2010). Summary, Conclusions and Prospects for Development. In: Linear, Time-varying Approximations to Nonlinear Dynamical Systems. Lecture Notes in Control and Information Sciences, vol 411. Springer, London. https://doi.org/10.1007/978-1-84996-101-1_12
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DOI: https://doi.org/10.1007/978-1-84996-101-1_12
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