Controller synthesis with guaranteed closed-loop phase constraints |
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Authors: | Wassim M Haddad VijaySekhar Chellaboina Behnood Gholami |
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Affiliation: | aSchool of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, United States;bMABE Department, University of Tennessee, Knoxville, TN 37996-2210, United States |
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Abstract: | In this paper, we present an analysis and synthesis approach for guaranteeing that the phase of a single-input, single-output closed-loop transfer function is contained in the interval −α,α] for a given α>0 at all frequencies. Specifically, we first derive a sufficient condition involving a frequency domain inequality for guaranteeing a given phase constraint. Next, we use the Kalman–Yakubovich–Popov theorem to derive an equivalent time domain condition. In the case where , we show that frequency and time domain sufficient conditions specialize to the positivity theorem. Furthermore, using linear matrix inequalities, we develop a controller synthesis approach for guaranteeing a phase constraint on the closed-loop transfer function. Finally, we extend this synthesis approach to address mixed gain and phase constraints on the closed-loop transfer function. |
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Keywords: | Phase constraints Gain constraints LMIs sciencedirect control" target="_blank">com/cache/MiamiImageURL/B6V21-4TVJ07S-1-65/0?wchp=dGLbVlW-zSkzk" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=11 width="24"/> control Kalman– Yakubovich– Popov equations Positivity theory |
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