Mapping of performance specification into parameter space for LTI systems is discussed from the perspective of the Lyapunov equation. After setting the main results on stability, corresponding formulations for a variety of performance criteria (e.g. settling time, damping and frequency-based criteria) are discussed. Thereby, the original performance mapping problem is transformed to a stability problem with modified system matrices that include free control and/or design parameters. The proposed performance mapping approach is demonstrated on two benchmark case studies of practical interest. (C) 2019 Elsevier Ltd. All rights reserved.