Abstract
This paper formulates sufficiency-type linear-output feedback decentralized closed-loop stabilization conditions if the continuous-time linear dynamic system can be stabilized under linear output-feedback centralized stabilization. The provided tests are simple to evaluate, while they are based on the quantification of the sufficiently smallness of the parametrical error norms between the control, output, interconnection and open-loop system dynamics matrices and the corresponding control gains in the decentralized case related to the centralized counterpart. The tolerance amounts of the various parametrical matrix errors are described by the maximum allowed tolerance upper-bound of a small positive real parameter that upper-bounds the various parametrical error norms. Such a tolerance is quantified by considering the first or second powers of such a small parameter. The results are seen to be directly extendable to quantify the allowed parametrical errors that guarantee the closed-loop linear output-feedback stabilization of a current system related to its nominal counterpart. Furthermore, several simulated examples are also discussed.
Highlights
Control systems are very important in real world applications and, they have been investigated exhaustively concerning their properties of stability, stabilization, controllability control strategies etc
Decentralized control is a useful tool for controlling dynamic systems by cutting some links between the dynamics coupling a set of subsystems integrated in the whole system at hand
It is claimed to give a non-complex method to test the feasibility of the implementation of decentralized control and conditions for its design, which be a fast and simpler stability test compared to Lyapunov stability theory [20,21], for instance, under a partial removal of information or physical cuts of links of coupling dynamics between the various subsystems or state, control and output components
Summary
Control systems are very important in real world applications and, they have been investigated exhaustively concerning their properties of stability, stabilization, controllability control strategies etc. The decentralized control design versus its decentralized control counterpart, under eventual output linear feedback, are studied from the point of view of the amount of information that can be lost or omitted in terms of the total or partial knowledge of the coupled dynamics between subsystems necessary in the decentralized case to keep the closed-loop stability. It is claimed to give a non-complex method to test the feasibility of the implementation of decentralized control and conditions for its design, which be a fast and simpler stability test compared to Lyapunov stability theory [20,21], for instance, under a partial removal of information or physical cuts of links of coupling dynamics between the various subsystems or state, control and output components.
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