Mixed l1/H∞ controllers for SISO discrete time systems

A successful controller design paradigm must take into account both model uncertainty and design specifications. Model uncertainty can be addressed using either H_∞ or l₁ robust control theory, depending upon the uncertainty characterization. However, these frameworks cannot accommodate the realistic case where the design specifications include both time and frequency domain constraints. In this paper the author addresses these problems using a mixed l₁/H_∞ approach. This approach allows for minimising the worst-case peak output due to a persistent disturbance, while, at the same time, satisfying an H_∞-norm constraint upon some closed-loop transfer function of interest. The main result of the paper shows that mixed l ₁/H_∞ optimal controllers can be obtained by solving a sequence of problems, each one consisting of a finite-dimensional convex optimisation and a standard, unconstrained H _∞ problem