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Controllability : A state of a system is said to be controllable if and only if the state value can be varied from any starting value to any finite value in finite time by application of an unbound input, then the state is said to be controllable. Y=x1+x2 is a completely controllable system.
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The concept of controllability refers to the ability of a controller to arbitrarily alter the functionality of the system plant. The state-variable of a system, x, represents the internal workings of the system that can be separate from the regular input-output relationship of the system.
Formally, a system is said to be observable if, for any possible sequence of state and control vectors (the latter being variables whose values one can choose), the current state (the values of the underlying dynamically evolving variables) can be determined in finite time using only the outputs.
Controllability is concerned with whether one can design control input to steer the state to arbitrarily values. Observability is concerned with whether without knowing the initial state, one can determine the state of a system given the input and the output. 3.1 Some linear mapping concepts.
In control theory, observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. The observability and controllability of a system are mathematical deals.
Controllability is concerned with whether one can design control input to steer the state to arbitrarily values. Observability is concerned with whether without knowing the initial state, one can determine the state of a system given the input and the output.
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