The paper addresses the problem of analysis and static output feedback control synthesis for strict quadratic dissipativity of linear time-invariant systems with state-space symmetry. As a particular case of dissipative systems, we consider the mixed H-infinity and positive real performance criterion and we develop an explicit expression for calculating the H-infinity norm of these systems. Subsequently, an explicit parametrization of the static output feedback control gains that solve the mixed H-infinity and positive real performance problem is obtained. Numerical examples demonstrate the use and computational advantages of the proposed explicit solutions. (C) 2009 Elsevier Ltd. All rights reserved.