It is common in parameter identification problem (or even dual parameter id + trajectories) to find solutions that give unstable systems, even when the measurement data comes from a stable system. If the system can be represented as a linear system about an equilibrium point, you could make constraints that enforce the real parts of the eigenvalues < 0. This would add new constraints and we'd need to find their Jacobian, which isn't so suitable for a symbolic method when the system order is high. Another option is to calculate the Routh table for the linear system, which effectively gives a set of inequality constraints that would guarantee stability. That may work for high order systems, even if the symbolic expressions get large. These are a couple of ideas for a subclass of parameter id problems for systems that are linearly stable. More ideas would be needed for nonlinear systems.