Controller synthesis with guaranteed closed-loop phase constraints

✍ Scribed by Wassim M. Haddad; VijaySekhar Chellaboina; Behnood Gholami

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 822 KB
• Volume: 44
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/j.automatica.2008.09.002

✦ Synopsis

In this paper, we present an analysis and synthesis approach for guaranteeing that the phase of a singleinput, 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 α = π 2 , 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.