H filtering via convex optimization

This paper reformulates the suboptimal (or level-gamma) H filtering problem into a Linear Matrix Inequality (LMI) problem by applying a bounded real lemma to the closed-loop transfer function. This formulation not only provides the condition of solvability but also constructs the suboptimal H filter. This formulation furthermore allows one to solve the 'epsilon-optimal' H filtering problem via convex optimization techniques, where the 'epsilon-optimality' implies that theH-norm of the resulting closed-loop transfer function is greater than or equal to the infimum, say gamma inf of the H-norms of all possible closed-loop transfer functions, but is less than or equal to epsilon gamma for an extremely small positive number epsilon, which will depend on the inf accuracy of the algorithms and the precision of a computer.