TABLE OF CONTENTS Generally, a dynamical system is characterized by a differential equation that gives a relation between the input and the output of that system. A dynamical system may be linear or nonlinear. It is said to be linear if the differential equation that characterizes the system is linear.
A differential equation is linear if the coefficients are constants or functions of only the independent variable and not that of the dependent variable. The most important property of the linear systems is the applicability of the principle of superposition, i.e, if y 1( t) and y 2( t) are two solutions to inputs r 1( t) and r 2( t), then the solution to the new input r( t) = c 1 r 1( t) + c 2 r 2( t) is given by y( t) = c 1 y 1( t) + c 2 y 2( t). This feature enables us to build system response to any complex input function by expressing it as a sum of several simple input functions.
A system is said to be nonlinear if the differential equation that characterizes it is nonlinear. A differential equation is nonlinear if it contains products or powers of the dependent variable or its derivatives. Nonlinear differential equations, in general, are quite difficult to solve. Furthermore, the property of superposition does not hold for nonlinear systems.
A control system...
