Stability of the zero solution of fuzzy delay differential equations via Lyapunov functions

This study considers the problem of how to guarantee the stability of systems whose behaviour is influenced by time delays and fuzzy parameters. We focus on fuzzy delay differential equations (FDDEs) and a framework based on Lyapunov-Krasovskii functionals. We derive delay – and fuzziness-dependent linear matrix inequalities that are easy to check with optimization software. These inequalities constitute conditions under which the zero solution of an FDDE is asymptotically stable at an exponential or [Formula: see text]-exponential rate. To show that the theory is more than a mathematical exercise, we test it on two examples. A temperature controlled chemical reactor with a thermal lag settles once criteria are imposed. In a second case, a market price model subject to constant information delay and fuzzy demand uncertainty drifts back to equilibrium in a p-exponential fashion that methods fail to capture. framework enlarges the certified stability region and demands less computational effort than Lyapunov approaches. These results suggest that engineers and economists can use the criteria as a design tool when delays and fuzzy parameters are unavoidable. Because the method relies only on standard optimization routines, it is readily extendable to adaptive, stochastic, or higher-dimensional settings, opening new avenues for robust controller synthesis and policy design.