Abstract
This paper presents a new method on the problem of organically structured control based on state observation for a class of large-scale systems with expanding construction. This problem is to design a local state feedback controller and an observer for a new subsystem which is added to a large-scale system without changing the decentralized state feedback control laws of the original construction, so that both the new subsystem and the resulting expanded system are robustly connectively stable. Firstly, based on state observers, the mathematical model of a large-scale system with expanding construction is reestablished and analyzed. In addition, the sufficient condition for robust decentralized connective stabilization of the expanded construction of large-scale systems is deduced by taking an LMI approach, which is further relaxed by removing the square matrix condition on the output matrix. This problem is transformed into solving an LMI problem. The new design method of an organically structured controller and observer for the expanded construction is also given. Finally, the simulation examples show the effectiveness of the proposed method.
Highlights
Structural changes of large-scale interconnected systems occur in real world applications, which have a negative impact on stability of the systems
Since the addition of new subsystems occurs during the operation of the original construction, it is more realistic to keep the decentralized control laws of the original subsystems unchanged
We have studied that the control design approach for original-construction subsystems is the same as the newly added subsystem, but the situation is often otherwise
Summary
Structural changes of large-scale interconnected systems occur in real world applications, which have a negative impact on stability of the systems. Due to the complexity of the frequency domain design, [6, 7] provided sufficient conditions for the solvability of the robust decentralized connective stabilization problem by taking LMI theory and proposed an organically structured control method for the expanded construction of large-scale systems. The observer-based decentralized controller was derived for large-scale systems with expanding construction in [14]. (1) An observerbased decentralized feedback controller is designed for a class of large-scale systems with expanding structure. Consider N subsystems in the original structure, which are controlled by state feedback with state observers. Mathematical Model of Large-Scale Systems with Expanding Construction Based on State Observation. Due to the newly added interconnections, the mathematical description of the original closed-loop system (6) can be modified as follows: AN−B−NLKNNCN] [XeNN].
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