Mixed l1/H∞ controllers for MIMO discrete-time systems

Presents a methodology for designing mixed l₁/H_∞ controllers for MIMO systems. These controllers allow for minimizing the worst-case peak output due to persistent disturbances, while, at the same time, satisfying an H_∞-norm constraint upon a given closed-loop transfer function. Therefore, these are of particular interest for applications dealing with multiple performance specifications. The main result of the paper shows that mixed l₁/H_∞ suboptimal controllers can be obtained by solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and a 4-block H _∞ problem. Thus, finding these solutions entails solving a finite dimensional convex optimisation problems and standard algebraic Riccati equations