Abstract
The distribution of water resources and the degree of economic development in different cities will result in different parameters for the supply and demand of domestic water in each city. In this paper, a simultaneous stabilization and robust control method is proposed for decision-making regarding multiple urban domestic water systems. The urban water demand is expressed as the product of the urban domestic water consumption population and per capita domestic water consumption. The fixed capital investment and labor input of the urban domestic water supply industry are used as control variables. Based on the Lyapunov stability theory and the linear matrix inequality method, multiple urban domestic water supply and demand systems can accomplish asymptotical stability through the coordinated input of investment and labor. For an empirical analysis, we take six cities—Nanjing, Wuxi, Nantong, Yangzhou, Xuzhou, and Lianyungang—in Jiangsu Province, China, to study the simultaneously stabilized coordinated control scheme. The simulation results show that the same control scheme simultaneously achieves the asymptotic stability of these urban domestic water supply and demand systems, and is robust when it comes to the variation of system parameters. This method is particularly suitable for a water resources administrative agency to make a unified decision-making arrangement for water supply input in different areas. It will help synchronize multiple urban domestic water managements and reduce the difficulty of control.
Highlights
In recent years, China’s urbanization rate has been continuously increasing
Since fixed capital investment and labor input are commonly used production factors, it is appropriate to take them as control variables to make simultaneously stabilized robust control decisions for multiple urban domestic water systems
In Reference [9], an optimal control model of water supply investment based on the time series of the urban water demand function is developed
Summary
China’s urbanization rate has been continuously increasing. According to the “2017 China statistical yearbook” (National Bureau of Statistics of China [1]), the urbanization rate in China was 46.99% in 2008, 49.95% in 2010, 56.10% in 2015, and 57.35% in 2016. This paper takes them as control variables to study the method for simultaneously stabilized robust control decisions for multiple urban domestic water systems This will help with the synchronization of water management in multiple cities. In order to simplify the control scheme and reduce the complexity of the control, for these m cities with different system parameters, it is desirable to design a unified decision-making method with I(t) and P(t) as control variables, such that the multiple urban domestic water supply and demand system can be asymptotically stable.
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