Discussion
State variable analysis is applicable to :
(1) LTI systems
(2) Time varying systems
(3) Non-linear systems
Which one of the following is/are correct ?
Answer: B
State variable analysis applies to all three, so the answer is (1), (2) and (3).
The state-space method describes a system by first-order differential equations in its state variables, \(\dot{x} = f(x, u, t)\). Unlike the transfer function, which is defined only for linear time-invariant systems with zero initial conditions, this form can handle linear time-invariant systems, time-varying systems (where the matrices depend on t) and non-linear systems (where f is a non-linear function), as well as multiple inputs and outputs.
The options that limit it to LTI systems, or leave out one class, describe the transfer-function approach rather than state variable analysis.
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