Energy-to-peak induced norm upper bound control approach for collocated structural systems

The current paper presents an explicit expression for an upper bound on the induced energy-to-peak norm for structural systems with collocated sensors and actuators. Using a linear matrix inequality (LMI)-based representation of the L-2-L-infinity norm of a collocated structural system, we determine an analytical upper bound on the L-2-L-infinity norm of such a system. The paper also addresses the problem of static output feedback controller design for such systems. By employing simple algebraic tools, we derive an explicit parametrization of feedback controller gains which guarantee a prescribed level of L-2-L-infinity performance for the closed-loop system. Finally, numerical examples are provided to validate the efficiency and benefits of the proposed techniques. The effectiveness of the obtained bound and control design methodology is evident, in problems involving very large scale structural systems where solving Lyapunov equation or LMIs with large number of decision variables is time-consuming or intractable.