An Algebraic Approach to Linear and Nonlinear Control

The analysis and design of control systems has been greatly influenced by the mathematical tools being used. Maxwell introduced linear differential equations in the 1860’s. Nyquist, Bode and others started the systematic use of tranfer functions, utilizing complex analysis in the 1930’s. Kalman brought forward state space analysis around 1960. For nonlinear systems, differential geometric concepts have been of great value recently. We will argue here that algebraic methods can be very useful for both linear and nonlinear systems. To give some motivation we will begin by looking at a few examples.

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