Constant signal tracking for state constrained dynamic systems

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Abstract
We deal with the possibility of tracking constant reference signals for a linear time-invariant dynamic system in the presence of state constraints. We resort to the theory of invariant sets due to their capability of well handling this kind of problems. We focus on the determination of suitable sets for the attainable steady state values and of suitable control laws which guarantee that every possible output steady state value belonging to this set can be reached from any initial state belonging to a proper set. Then, based on recent results on the possibility of associating to these explicit smooth control laws, we derive an explicit controller which allows the system to asymptotically track constant reference signals and guarantees that no constraint violation occurs. Finally, we report an example of the implementation of the proposed control law.