Explicit solutions for stabilization and H∞ control of time-delayed state-space symmetric systems

The paper examines the stabilization and the H_∞ norm performance analysis and control of state-delayed systems with a symmetric state-space realization. Such symmetric realizations appear in many engineering applications. By exploiting the state-space symmetry, we obtain an explicit solution for a bound on the H_∞ norm of such symmetric time-delayed systems. Also, we derive an explicit parametrization of static output feedback gains that solve the stabilization and H_∞ control synthesis problems. Computational examples are used to demonstrate the significance and validity of the proposed methods and results.