Unified approach for Euler–Lagrange equation arising in calculus of variations

We address the development of a unified approach for the necessary conditions for optimization of a functional arising in calculus of variations. In particular, we develop a unified approach for the Euler–Lagrange equation, that is simultaneously applicable to both shift ( q )‐operator‐based discrete‐time systems and the derivative (d/d t )‐operator‐based continuous‐time systems. It is shown that the Euler–Lagrange results that are now obtained separately for continuous‐ and discrete‐time systems can be easily obtained from the unified approach. An illustrative example is given. Copyright © 2005 John Wiley & Sons, Ltd.