On the distributed stable full information H∞ minimax problem

✍ Scribed by Olof J. Staffans

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 351 KB
• Volume: 8
• Category: Article
• ISSN: 1049-8923
• DOI: 10.1002/(sici)1099-1239(19981230)8:15<1255::aid-rnc386>3.0.co;2-p

✦ Synopsis

We study the distributed parameter suboptimal full information H problem for a stable well-posed linear system with control u, disturbance w, state x, and output y. Here u, w, and y are ¸-signals on (0, R) with values in the Hilbert spaces º, ¼, and ½, and the state x is a continuous function of time with values in the Hilbert space H. The problem is to determine if there exists a (dynamic) -suboptimal feedforward compensator, i.e., a compensator U such that the choice u"Uw makes the norm of the input/output map from w to y less than a given constant . A sufficient condition for the existence of a -suboptimal compensator is that an appropriately extended input/output map of the system has a (J, S)-inner-outer factorization of a special type, and if the control and disturbance spaces are finite-dimensional and the system has an ¸ impulse response, then this condition is also necessary. Moreover, in this case there exists a central state feedback/feedforward controller, which can be used to give a simple parameterization of the set of all -suboptimal compensators. Our proof use a game theory approach.