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Robust $$H_\infty$$ control for a generic linear rational expectations model of economy. (English) Zbl 1193.93092
Summary: Large time-delay and small disturbance attenuation are very important for macroeconomic systems. This paper is concerned with the problem of robust $$H_\infty$$ control with large time-delay and small disturbance attenuation for a generic linear rational expectations model of economy with uncertainties, time-varying delay and random shocks. The norm bounded uncertainties are used to describe the uncertainties of economic system. The concept of two levels of conservatism and the approach of Parameters Weak Coupling Linear Matrix Inequalities (PWCLMIs) are developed in this paper. The result is presented in terms of PWCLMIs in this note. Large time-delay and small disturbance attenuation are achieved without increasing conservatism of result. Furthermore, according to the robust $$H_\infty$$ result, one will obtain various results readily by employing different games. An example is given to show the benefit of the presented approach.

##### MSC:
 93B35 Sensitivity (robustness) 91B74 Economic models of real-world systems (e.g., electricity markets, etc.) 93C15 Control/observation systems governed by ordinary differential equations 34H05 Control problems involving ordinary differential equations
Duali
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