On finding the minimum possible peak value of multi-input infinite-horizon steering controls

A computational method for the infinite-dimensional optimization problem of finding the minimum possible peak value of a multi-input infinite-horizon steering control is presented. It is shown that the problem is equivalent to a convex program in a finite-dimensional Euclidean space. The convex program is approximated by a sequence of linear programs, the objective values of which converge to the objective of the convex program. A bound above and below are given for the error between the objective value of the convex program and the objective of any linear program in the approximating sequence. The bounds show convergence and are geometric with ratio given by the minimum modulus over all unstable plant poles