Adjoint operator-based isomorphism realisation and control design for non-linear systems

In this study, a realisation to robust right coprime factorisation and robust stability of non-linear systems with unknown bounded perturbations are investigated based on inner product of Hilbert spaces. In detail, first, a feasible framework based on inner product is proposed to study robust right factorisation of the perturbed non-linear systems, which provides fundamental for factorising the systems and guaranteeing robust stability. Second, a condition based on adjoint operators of Hilbert spaces is given for the non-linear systems with unknown bounded perturbations, according to which a compensator is designed and meanwhile eliminates difficulties in obtaining internal signal of the perturbed non-linear systems. After that, a realisable design scheme on robust stability is given based on the designed controller and the unimordular property. According to the proposed robust design scheme, the non-linear systems with unknown bounded perturbations can be handled precisely and effectively. Finally, a simulation example is given to confirm the effectiveness of the proposed methods.