lsim and lsimplot has problems with arguments u and x0

See https://discourse.julialang.org/t/controlsystems-transfer-functions-with-delay/58003/7

• Inconsistency between normal and delayed systems in how u is defined, u(x, t) vs u(t). Can easily lead to defining a zero input since delay system also accept u(uout, t) as an inplace version.
• Missing documentation in the online docs about lsim for delayed systems, exists in help?> menu in repl
• Does not handle different types for x0, for example if sys is float and x0 is int array
• lsimplot can't handle x0 at all and gives strange error message
• Not very clear what the states are, i.e. how the delay enters the system. This is important when setting the initial state x0. It is also not very clear how the delayed states are initialized and how you can affect them (not really possible as it is now but maybe it should be).

Start by reading the lsim and lsimplot entry points, then compare the delayed-system guidance in the online documentation with the help? text. Done means the u and x0 behavior is consistent and documented, lsimplot handles x0, and the state and delayed-state initialization semantics are clear.