A time-domain penalty function approach to mixed H/sub 2//H/sub /spl infin//-control using parameter optimization methods

In this paper we consider the problem of minimum nominal H/sub 2/-norm with H/sub /spl infin//-constraints for systems with multiple operating points. The performance measure is defined as a weighted sum of the corresponding nominal H/sub 2/-norms while robust stability of the individual closed-loop systems is defined in terms of a H/sub /spl infin//-bound for each plant condition. In this paper we define a new time-domain scalar cost function J/sub /spl infin//(t/sub f/) representing the H/sub /spl infin//-bounds in an overall cost function for the mixed H/sub 2//H/sub /spl infin//-design. J/sub /spl infin//(t/sub f/) is, for finite time t/sub f/, a penalty function and, for t/sub f//spl rarr//spl infin/, a barrier function. Using J/sub /spl infin//(t/sub f/), the mixed H/sub 2//H/sub /spl infin//-design problem results in an unconstrained optimization problem, that, for t/sub f//spl rarr//spl infin/, recovers the original objective of minimizing the performance measure subject to the H/sub /spl infin//-bounds. The resulting optimization problem is smooth and hence standard gradient-based software can be applied. The class of controllers considered includes proper and strictly proper LTI controllers with fixed structure and/or fixed order.<>