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Controllability is an important property of a control system and plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control. Controllability and observability are dual aspects of the same problem.
One of the many ways one can achieve such goal is by the use of the Controllability Gramian. Controllability in LTI Systems. Linear Time Invariant (LTI) ...
Observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. In control theory, the observability and controllability of a linear system are mathematical duals.
Controllability and observability are main issues in the analysis of a system before deciding the best control strategy to be applied, or whether it is even possible to control or stabilize the system. Controllability is related to the possibility of forcing the system into a particular state by using an appropriate control signal.
In control theory and in particular when studying the properties of a linear time-invariant system in state space form, the Hautus lemma (after Malo L. J. Hautus), also commonly known as the Popov-Belevitch-Hautus test or PBH test, [1] [2] can prove to be a powerful tool.
While controllability and observability improvements for internal circuit elements definitely are important for test, they are not the only type of DFT. Other guidelines, for example, deal with the electromechanical characteristics of the interface between the product under test and the test equipment.
Controllability: The degree to which it is possible to control the state of the component under test (CUT) as required for testing. Observability: The degree to which it is possible to observe (intermediate and final) test results. Isolateability: The degree to which the component under test (CUT) can be tested in isolation.
The Observability Gramian can be found as the solution of the Lyapunov equation given by + = In fact, we can see that if we take = as a solution, we are going to find that: + = + = = | = = =