Static controller synthesis for peak-to-peak gain minimization as an optimization problem

An optimization approach to linear control systems has recently become very popular. For example, the linear feedback matrix in the classical linear-quadratic regulator problem can be viewed as a variable, and the problem can be reduced to the minimization of the performance indicator for this variable. To this end, one can apply the gradient method and obtain a justification of the convergence. This approach has been successfully applied to a number of problems, including output feedback optimization. The present paper is the first to apply this approach to the peak-to-peak gain minimization problem. A gradient method for finding a static state or output feedback is written out and justified. A number of examples are considered, including the single and double pendulums.