Explicit solutions for collocated structural control with guaranteed H2 norm performance specifications

This paper presents explicit solutions for velocity feedback control of structural systems with collocated sensors and actuators to satisfy closed-loop H-2 and L-2 - L-infinity norm performance specifications. First, we consider an open-loop collocated structural system and obtain upper bounds for the H-2 and L-2 - L-infinity system norms using a solution for the linear matrix inequality formulation of the norm analysis conditions. Next, we address the problem of static output velocity feedback controller design for such systems. By employing simple algebraic tools, we derive an explicit parametrization of the controller gains which guarantee a prescribed level of H-2 or L-2 - L-infinity norm performance of the closed-loop system. Finally, numerical examples are presented to validate the advantages of the proposed techniques. The effectiveness of the proposed bounds and output feedback control design methods become apparent, especially in very large-scale structural systems where control design methods based on the solution of Lyapunov or Riccati equations are time-consuming or intractable.