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What is an LTI System ?

The basic representation for linear systems is the linear state equation, customarily written in the standard form

(1)

where the overdot denotes differentiation with respect to time t. The vector function of time x(t) is called the state vector, and its components, , are the state variables. The input signal is the function u(t), and y(t) is the output signal. We assume throughout that .

Default assumptions on the coefficient matrices in (1) are that the entries of , and are continuous, real-valued functions defined for all . Standard terminology is that (1) is linear time invariant (LTI) if these coefficient matrices are constant. The linear state equation is called time varying if any coefficient matrix varies with time.


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