H₂ Control Performance Limitations for SIMO Linear Discrete-Time Systems

Abstract

This paper is concerned with intrinsic control performance limitations achievable by feedback for single-input and multi-output (SIMO) possibley unstable and non-minimum phase linear discrete-time systems. We investigate two typical H₂ optimal control problems, namely optimal tracking control problem and minmal energy control problem. We derive closed-form analytical expressions of the best achievable tracking error and minmal energy H₂ norms. The former consists of plant gain as well as unstable poles and non-minimum phase zeros of the plant, while the latter is only given by unstable poles and non-minimum phase zeros of the plant. Those results are confirmed by several numerical examples, and they characterize easiness and difficulty of plants to be controlled.