A novel approach is proposed towards on-line and real-time detection and isolation of parametric faults in a multivariable linear continuous-time (CT) system. The problem of fault detection and isolation (FDI) is formulated in terms of a CT state space model. Since parameters in a CT model usually have simple relationships with physical parameters of the system, isolating parametric faults in the CT model can lead to the isolation of undesired changes in the physical parameters. Isolating parametric faults is very challenging, because even in a linear time-invariant system, the fault model can be time-varying and random. To obtain a constant fault model, many existing parametric FDI schemes have to make unrealistical assumptions. Our proposed FDI approach can generate an optimal primary residual vector (PRV), in which the fault model is constant without making any assumptions. To isolate faults, the PRV is transformed into a set of structured residual vectors (SRVs), where one SRV is made insensitive to a specified subset of faults, but most sensitive to other faults. The proposed approach is successfully applied to detection and isolation of undesired changes in the physical parameters of a simulated continuously stirred tank process.