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Lessons in Estimation Theory for Signal Processing, Communications, and Control, Second Edition by Jerry M. Mendel - Department of Electrical Engineering, University of Southern California, Los Angeles, California

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Lesson 23 Linearization and Discretization of Nonlinear Systems

Summary

Many real-world systems are continuous-time in nature and quite a few are also nonlinear. The purpose of this lesson is to explain how to linearize and discretize a nonlinear differential equation model. We do this so that we will be able to apply our digital estimators to the resulting discrete-time system.

A nonlinear dynamical system is linearized about nominal values of its state vector and control input. For example, x*(t) denotes the nominal value of x(t); it must provide a good approximation to the actual behavior of the system. The approximation is considered good if the difference between the nominal and actual solutions can be described by a set of linear differential ...

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