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Feedback passivity of nonlinear discrete-time systems with direct input-output link. (English) Zbl 1077.93045

This paper deals with the passification problem for nonlinear, discrete-time systems of the form \[ x(k+1)= f(x(k), u(k)),\quad y(k)= h(x(k),u(k)), \] where \(f\) and \(h\) are smooth maps vanishing at \(x= u= 0\). The main result asserts that if the relative degree of the system is zero and there exist locally passive zero dynamics with a positive definite storage function of class \(C^2\), then the system can be rendered passive by applying a regular feedback. The case of affine systems is considered with special attention.

MSC:

93D15 Stabilization of systems by feedback
93C55 Discrete-time control/observation systems
93D25 Input-output approaches in control theory
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[1] Byrnes, C. I.; Isidori, A.; Willems, J. C., Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems, IEEE Transactions on Automatic Control, 36, 1228-1240 (1991) · Zbl 0758.93007
[2] Byrnes, C. I., & Lin, W. (1993). Discrete-time lossless systems, feedback equivalence, and passivity. Proceedings of the IEEE 32nd conference on decision and control; Byrnes, C. I., & Lin, W. (1993). Discrete-time lossless systems, feedback equivalence, and passivity. Proceedings of the IEEE 32nd conference on decision and control
[3] Byrnes, C. I.; Lin, W., Losslessness, feedback equivalence, and the global stabilization of discrete-time nonlinear systems, IEEE Transactions on Automatic Control, 39, 1, 83-98 (1994) · Zbl 0807.93037
[4] Lin, W. (1993). Synthesis of discrete-time nonlinear systems; Lin, W. (1993). Synthesis of discrete-time nonlinear systems
[5] Monaco, S., & Normand-Cyrot, D. (1987). Minimum-phase nonlinear discrete-time systems and feedback stabilization. Proceedings of the 26th conference on decision and control; Monaco, S., & Normand-Cyrot, D. (1987). Minimum-phase nonlinear discrete-time systems and feedback stabilization. Proceedings of the 26th conference on decision and control
[6] Monaco, S.; Normand-Cyrot, D., Zero dynamics of sampled nonlinear systems, Systems and Control Letters, 11, 229-234 (1988) · Zbl 0664.93037
[7] Monaco, S., & Normand-Cyrot, D. (1999). Nonlinear representations and passivity conditions in discrete time. In Robustness in identification and controlLecture notes in control and information sciences; Monaco, S., & Normand-Cyrot, D. (1999). Nonlinear representations and passivity conditions in discrete time. In Robustness in identification and controlLecture notes in control and information sciences · Zbl 0948.93518
[8] Navarro-López, E. M. (2002). Dissipativity and passivity-related properties in nonlinear discrete-time systems; Navarro-López, E. M. (2002). Dissipativity and passivity-related properties in nonlinear discrete-time systems
[9] Navarro-López, E. M., & Fossas-Colet, E. (2002). Dissipativity, passivity and feedback passivity in the nonlinear discrete-time setting. 15th IFAC world congress; Navarro-López, E. M., & Fossas-Colet, E. (2002). Dissipativity, passivity and feedback passivity in the nonlinear discrete-time setting. 15th IFAC world congress
[10] Navarro-López, E. M., Fossas-Colet, E., & Cortés, D. (2002a). Local feedback dissipativity and dissipativity-based stabilization of nonlinear discrete-time systems. Latin American conference on automatic control; Navarro-López, E. M., Fossas-Colet, E., & Cortés, D. (2002a). Local feedback dissipativity and dissipativity-based stabilization of nonlinear discrete-time systems. Latin American conference on automatic control
[11] Navarro-López, E. M.; Sira-Ramı́rez, H.; Fossas-Colet, E., Dissipativity and feedback dissipativity properties of general nonlinear discrete-time systems, European Journal of Control. Special Issue: Dissipativity of Dynamical Systems. Application in Control, 8, 3, 265-274 (2002) · Zbl 1293.93614
[12] Willems, J. C., Dissipative dynamical systems. Part I: General theory. Part IILinear systems with quadratic supply rates, Archive for Rational Mechanics and Analysis, 45, 5, 321, 351, 352.393 (1972)
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