New Solution of Induced L ∞ Optimal Control

The main propose of this paper, is performing a new solution on the basis of Linear Matrix Inequality (LMI) for designing induced ∞ l optimal controllers. Induced ∞ l optimal control allows directly time-domain specifications into the controller synthesis procedure and furnishes a complete solution to the robust performance problem. The new technique, which is proposed as an algorithm, combines the original concept of peakto-peak gain of designed system with optimal control theory and employs a free design parameter allowing for a flexible management of the tradeoff between robustness to disturbance signals and magnitude of the worst peak-to-peak gain of the designed system. For the convergence of this algorithm, a scope is found on the basis of the H ∞ − norm. If the length of this interval is small, we have a good estimate of the actual optimal peak-topeak gain that is achievable by control.