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I'm trying to think of limitations or disadvantages of LTI systems in control theory, however, I can't think of many. The only one I can think of is that not every system is an LTI system.

Linear time-invariant systems (LTI systems) are a class of systems used in signals and systems that are both linear and time-invariant. Linear systems are systems whose outputs for a linear combination of inputs are the same as a linear combination of individual responses to those inputs. Time-invariant systems are systems where the output does not depend on when an input was applied. These properties make LTI systems easy to represent and understand graphically.

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The advantage of a Linear Time Invariant (LTI) system is that it is easy to work with. It's the most simple type of dynamic system and we have a lot of theory available for it. As soon as you start dropping the time invariance or linearity you get a more general class of systems which is harder to analyze and design controller for which garantuee stability/performance.

The disadvantage of LTI systems is that they do not exist. Nothing in the real world is linear or time-invariant so it is an approximation for your system. How good the approximation is, depends on what accuracy you need from your model.

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  • $\begingroup$ Thanks, I guess that's the only disadvantage of an LTI system. I think I have to come up with an example why LTI system descriptions don't always work or lead to a poor controller design. $\endgroup$
    – Paperreader
    Jun 18, 2020 at 19:24
  • $\begingroup$ That's very easy. Take a nonlinear system e.g. pendulum linearize it around one equilibrium point. The farther away from the equilibrium point the less accurate linear model will describe the actual dynamics. Or make the length of the pendulum time depending. Or a system with nonlinear damping, hysteresis, backlash, saturation, etc. Just something nonlinear and the linear system will not describe it accurately if you exceed a certain tresshold. $\endgroup$
    – useless-machine
    Jun 18, 2020 at 21:35

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