An H2 Upper Bound Approach for Control of Collocated Structural Systems

This paper presents an explicit expression for an upper bound on the H₂ norm for structural systems with collocated sensors and actuators. First, we consider an open-loop collocated structural system and obtain an upper bound for the H₂ norm using a particular solution for the linear matrix inequality formulation of the H₂ norm analysis conditions. Next, we address the problem of static output feedback controller design for such systems. By employing simple algebraic tools, we derive an explicit parametrization of controller gains which guarantee a prescribed H₂ norm performance of the closed-loop system. At last, numerical examples are provided to validate the advantages of the proposed techniques. The effectiveness of the proposed bound and control design method becomes apparent, especially in very large scale structural systems where using classical methods of solving Lyapunov and Riccati equations are time-consuming or intractable.