We consider the problem of transforming two linear control systems to a form with relative degree by one and the same linear time-invariant change of outputs. A constructive algorithm is proposed that permits one to verify if this problem has a solution, and if it does, find the desired change. Moreover, it is shown that transforming three control systems by one and the same linear time-invariant change of outputs to a form with relative degree is not always possible.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Isidori, A., Nonlinear Control Systems, London: Springer, 1995.
Mueller, M., Normal form for linear systems with respect to its vector relative degree, Linear Algebra Its Appl., 2009, vol. 480, no. 4, pp. 1292–1312.
Wang, L., Isidori, A., and Su, H., Global stabilization of a class of invertible MIMO nonlinear systems, IEEE Trans. Autom. Control, 2015, vol. 60, no. 3, pp. 616–631.
Wang, L., Isidori, A., Liu, Z., and Su, H., Robust output regulation for invertible nonlinear MIMO systems, Automatica, 2017, vol. 82, pp. 278–286.
Il’in, A.V., Korovin, S.K., and Fomichev, V.V., Metody robastnogo obrashcheniya dinamicheskikh sistem (Methods for Robust Inversion of Dynamical Systems), Moscow: Fizmatlit, 2009.
Goncharov, O.I. and Fomichev, V.V., Observer for multivariable systems of arbitrary relative order, Comput. Math. Model., 2013, vol. 24, no. 2, pp. 182–202.
Fomichev, V.V. and Korovin, S.K., Nablyudateli sostoyaniya dlya lineinykh sistem s neopredelennost’yu (State Observers for Linear Systems with Uncertainty), Moscow: Fizmatlit, 2007.
Isidori, A., The zero dynamics of a nonlinear system: from the origin to the latest progresses of a long successful story, Proc. 30th Chin. Control Conf. (Yantai, China, 2011), pp. 18–25.
Kraev, A.V., Rogovskiy, A.I., and Fomichev, V.V., On a generalization of relative degree, Differ. Equations, 2014, vol. 50, no. 8, pp. 1128–1132.
Tanwani, A., Dominguez-Garcia, A., and Liberzon, D., An inversion-based approach to fault detection and isolation in switching electrical networks, IEEE Trans. Contr. Syst. Tech., 2011, vol. 19, pp. 1059–1074.
Fomichev, V.V., Kraev, A.V., and Rogovskiy, A.I., Transformation of hyperoutput systems to a form with relative degree, Differ. Equations, 2020, vol. 56, no. 11, pp. 1472–1484.
This work was supported by the Russian Foundation for Basic Research, project no. 18-07-00540 and facilitated by the Moscow Center for Fundamental and Applied Mathematics.
Translated by V. Potapchouck
About this article
Cite this article
Kraev, A.V., Rogovskiy, A.I. Simultaneous Transformation of Systems to a Form with Relative Degree. Diff Equat 56, 1644–1649 (2020). https://doi.org/10.1134/S00122661200120137