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 L2 - L∞ norm of a collocated structural system, we determine an analytical upper bound
on the L2 - L∞ 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 L2 - L∞ performance for the closed-loop system.
Finally, numerical examples are provided to validate the effciency 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.
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