Robust peak gain problem for uncertain systems via LMI approach

This paper deals with the problem of robust peak-to-peak gain minimization (the L₁ or L_∞ induced norm problem) for finite-dimensional LTI uncertain systems. By minimizing an upper bound of the induced L_∞-norm, we propose a controller synthesis method for uncertain systems. The controller synthesis is reduced to minimizing a continuous function of a single real variable. State-feedback and output-feedback controllers are obtained by using the linear matrix inequality (LMI) approach, and the controllers have at most the same order as the plant. Our result shows that if there exists a linear dynamic state-feedback controller that achieves a certain level of performance, then there exists a static, linear, state-feedback controller that also achieves this level of performance, and vice versa. This is also equivalent to solvability of the LMI problem.