H∞H∞ control of fractional linear systems

In this paper, the standard H∞H∞ control problem for continuous-time fractional linear time-invariant single-input–single-output systems is solved. The adopted approach consists of extending to the fractional case the procedure followed within the classical solution for the integer case. According to the classical route, we first consider the generalization to fractional systems of the standard Youla parameterization of all the stabilizing controllers. The H∞H∞ optimal controller is then found among the class of stabilizing controllers, recasting the control problem into a model-matching one. The results obtained naturally extend well-established results to a fractional setting, including both the commensurate and noncommensurate case, thus providing a framework where H∞H∞ design can be recast along the well-known and fruitful lines of the integer case. A worked-through example is discussed in detail to illustrate the design procedure.