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.
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.