Artículos de revistas
Characterising Discrete-time Linear Systems With The "mixed" Positive Real And Bounded Real Property
Registro en:
European Journal Of Control. European Control Association, v. 20, n. 5, p. 259 - 268, 2014.
9473580
10.1016/j.ejcon.2014.07.002
2-s2.0-84908206642
Autor
Souza M.
Griggs W.M.
Ordonez-Hurtado R.H.
Sajja S.S.K.
Lanzon A.
Shorten R.N.
Institución
Resumen
In this paper, we present characterisations of linear, shift-invariant, discrete-time systems that exhibit mixtures of small gain-type properties and positive real-type behaviours in a certain manner. These "mixed" systems are already fairly well characterised in the continuous-time domain, but the widespread adoption of digital controllers makes it necessary to verify whether commonly used discretisation procedures preserve the characteristic of "mixedness". First, we analyse the effects of classical discretisation methods on the "mixed" property using Nyquist methods. A frequency domain feedback stability result is then presented. Finally, we develop a spectral-based characterisation of "mixed" discrete-time systems which provides a practical computational test that can also be applied to the MIMO case. Several examples validate the developed theory. 20 5 259 268 Anderson, B.D.O., Failures of adaptive control theory and their resolution (2005) Commun. Inf. Syst., 5 (1), pp. 1-20 Anderson, B.D.O., Moore, J.B., (2007) Optimal Control: Applications and Methods, , Dover Publications, Mineola, NY Anderson, B.D.O., Vongpanitlerd, S., (2006) Network Analysis and Synthesis: A Modern Systems Theory Approach, , Dover, Mineola, NY A˚ström, K.J., Wittenmark, B., (1997) Computer-Controlled Systems: Theory and Design, 3rd Ed., , Prentice Hall, Upper Saddle River, NJ Bao, J., Lee, P.L., Wang, F., Zhou, W., New robust stability criterion and robust controller synthesis (1998) Int. J. Robust Nonlinear Control, 8 (1), pp. 49-59 Borrelli, F., Bemporad, A., Fodor, M., Hrovat, D., An MPC/hybrid system approach to traction control (2006) IEEE Trans. Control Syst. Technol., 14 (3), pp. 541-552 Costa-Castelló, R., Wang, D., Griñó, R., A passive repetitive controller for discrete-time finite-frequency positive-real systems (2009) IEEE Trans. Autom. Control, 54 (4), pp. 800-804 Corless, M., Shorten, R., On a class of generalized eigenvalue problems and equivalent eigenvalue problems that arise in systems and control theory (2011) Automatica, 47 (3), pp. 431-442 Chen, T., Francis, B.A., (1995) Optimal Sampled-Data Control Systems, , Springer-Verlag, London, UK Desoer, C.A., Vidyasagar, M., (1975) Feedback Systems: Input-Output Properties, , Academic Press, New York and London Falcone, P., Tseng, H.E., Borrelli, F., Asgari, J., Hrovat, D., MPC-based yaw and lateral stabilisation via active front steering and braking (2008) Vehicle Syst. Dyn., 46, pp. 611-628 Fantoni, I., Lozano, R., Spong, M.W., Energy based control of the Pendubot (2000) IEEE Trans. Autom. Control, 45 (4), pp. 725-729 Franklin, G.F., Powell, J.D., Emami-Naeini, A., (2002) Feedback Control of Dynamic Systems, 4th Ed., , Prentice Hall, Upper Saddle River, NJ Glad, T., Ljung, L., (2000) Control Theory: Multivariable and Nonlinear Methods, , Taylor & Francis, London and New York Golub, G.H., Van Loan, C.F., (1996) Matrix Computations, 3rd Ed., , Johns Hopkins University Press, Baltimore, MD Griffiths, P.G., Gillespie, R.B., Freudenberg, J.S., A fundamental linear systems conflict between performance and passivity in haptic rendering (2011) IEEE Trans. Robotics, 27 (1), pp. 75-88 Griggs, W.M., Anderson, B.D.O., Lanzon, A., A "mixed" small gain and passivity theorem in the frequency domain (2007) Syst. Control Lett., 56 (9-10), pp. 596-602 Griggs, W.M., Anderson, B.D.O., Lanzon, A., Rotkowitz, M.C., Interconnections of nonlinear systems with "mixed" small gain and passivity properties and associated input-output stability results (2009) Syst. Control Lett., 58 (4), pp. 289-295 Griggs, W.M., Anderson, B.D.O., Shorten, R.N., A test for determining systems with "mixed" small gain and passivity properties (2011) Syst. Control Lett., 60 (7), pp. 479-485 Griggs, W.M., Sajja, S.S.K., Anderson, B.D.O., Shorten, R.N., On interconnections of "mixed" systems using classical stability theory (2012) Syst. Control Lett., 61 (5), pp. 676-682 Hespanha, J.P., Naghshtabrizi, P., Xu, Y., A survey of recent results in networked control systems (2007) Proc. IEEE Special Issue Technol. Netw. Control Syst., 95 (1), pp. 138-162 Iwasaki, T., Hara, S., Yamauchi, H., Dynamical system design from a control perspective: Finite frequency positive-realness approach (2003) IEEE Trans. Autom. Control, 48 (8), pp. 1337-1354 Iwasaki, T., Hara, S., Fradkov, A.L., Time domain interpretations of frequency domain inequalities on (semi)finite ranges (2005) Syst. Control Lett., 54 (7), pp. 681-691 Lancaster, P., Tismenetsky, M., (1985) The Theory of Matrices with Applications, , Academic Press, San Diego and London Marquez, H.J., (2003) Nonlinear Control Systems: Analysis and Design, , John Wiley & Sons, Hoboken, NJ Meyer, C.D., (2000) Matrix Analysis and Applied Linear Algebra, , SIAM, Philadelphia, PA Nehari, Z., (1975) Conformal Mapping, , Dover Publications, New York, NY Noble, B., Daniel, J.W., (1988) Applied Linear Algebra, , Prentice Hall, Englewood Cliffs, NJ Oishi, Y., Passivity degradation under the discretization with the zero-order hold and the ideal sampler Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, GA, USA, 2010, pp. 7613-7617 Ortega, R., Spong, M.W., Adaptive motion control of rigid robots: A tutorial Proceedings of the 27th IEEE Conference on Decision and Control, Austin, TX, USA, 1988, pp. 1575-1584 Patra, S., Lanzon, A., Stability analysis of interconnected systems with "mixed" negative-imaginary and small-gain properties (2011) IEEE Trans. Autom. Control, 56 (6), pp. 1395-1400 Pietrus, A., Veliov, V.M., On the discretization of switched linear systems (2009) Syst. Control Lett., 58 (6), pp. 395-399 Postlethwaite, I., Edmunds, J.M., MacFarlane, A.G.J., Principal gains and principal phases in the analysis of linear multivariable feedback systems (1981) IEEE Trans. Autom. Control, 26 (1), pp. 32-46 Rohrs, C.E., Valavani, L., Athans, M., Stein, G., Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics (1985) IEEE Trans. Autom. Control, 30 (9), pp. 881-889 Santina, M., Stubberud, A.R., Discrete-time systems (2011) The Control Handbook: Control System Fundamentals, 2nd Ed., , W.S. Levine (Ed.), CRC Press, Boca Raton, FL Sanfelice, R.G., Teel, A.R., Dynamical properties of hybrid systems simulators (2010) Automatica, 46 (2), pp. 239-248 Santina, M.S., Stubberud, A.R., Hostetter, G.H., Discrete-time equivalents to continuous-time systems (1996) The Control Handbook, 1st Ed., , W.S. Levine (Ed.), CRC Press, Boca Raton, FL Seron, M.M., Braslavsky, J.H., Goodwin, G.C., (1997) Fundamental Limitations in Filtering and Control, , Springer-Verlag, London, UK Shorten, R.N., Curran, P., Wulff, K., Zeheb, E., A note on spectral conditions for positive realness of transfer function matrices (2008) IEEE Trans. Autom. Control, 53 (5), pp. 1258-1261 Shorten, R., Corless, M., Sajja, S., Solmaz, S., On Padé approximations, quadratic stability and discretization of switched linear systems (2011) Syst. Control Lett., 60 (9), pp. 683-689 Smith, M.C., Synthesis of mechanical networks: The inerter (2002) IEEE Trans. Autom. Control, 47 (10), pp. 1648-1662 Teel, A.R., Georgiou, T.T., Praly, L., Sontag, E.D., Input-output stability (2011) The Control Handbook: Control System Advanced Methods, 2nd Ed., , W.S. Levine (Ed.), CRC Press, Boca Raton, FL Tóth, R., Heuberger, P.S.C., Van Den Hof, P.M.J., Discretisation of linear parameter-varying state-space representations (2010) IET Control Theory Appl., 4 (10), pp. 2082-2096 Tóth, R., Lovera, M., Heuberger, P.S.C., Corno, M., Van Den Hof, P.M.J., On the discretisation of linear fractional representations of LPV systems (2012) IEEE Trans. Control Syst. Technol., 20 (6), pp. 1473-1489 Wen, J.T., Arcak, M., A unifying passivity framework for network flow control (2004) IEEE Trans. Autom. Control, 49 (2), pp. 162-174 Xie, L., Fu, M., Li, H., Passivity analysis and passification for uncertain signal processing systems (1998) IEEE Trans. Signal Process., 46 (9), pp. 2394-2403 Xiong, J., Petersen, I.R., Lanzon, A., Finite frequency negative imaginary systems (2012) IEEE Trans. Autom. Control, 57 (11), pp. 2917-2922 Zappavigna, A., Colaneri, P., Kirkland, S., Shorten, R., Essentially negative news about positive systems (2012) Linear Algebra Appl., 436 (9), pp. 3425-3442 Zhou, K., Doyle, J.C., Glover, K., (1996) Robust and Optimal Control, , Prentice Hall, Upper Saddle River, NJ