The composite matrix used in controllability test of the system is
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Controllability stabilizes an unstable system. Thus, we can say a dynamic system that does not offer, transferring one state to another is not a controllable system. As the theory of controllability was proposed by Kalman, thus a test named Kalman's test is used to determine whether the system is controllable or not.
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Controllability measures the ability of a particular actuator configuration to control all the states of the system; conversely, observability measures the ability of the particular sensor configuration to supply all the information necessary to estimate all the states of the system.
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