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A new periodic multirate model reference adaptive controller for possibly non stably invertible plants. (English) Zbl 0933.93049
The paper deals with the model reference control of linear continuous-time systems with unknown parameters. The authors explore the possibility of extending the multirate-input controller (MRIC) approach proposed recently by the first author and P. N. Paraskevopoulos [ Proc. 2nd E.C.C., Groningen, The Netherlands, Vol. 3, 1648-1652 (1992)] to control linear time-invariant plants with unknown parameters. On the basis of the MRIC approach, which is considered as an alternative to standard dynamic compensation, the solution to the model matching problem is reduced to the solution to a non-homogeneous algebraic matrix equation rather than a polynomial diophantine equation required in the standard indirect model reference adaptive technique. Finally, persistency of excitation of the continuous-time plant under control is ensured without special assumption on the reference signal and the only a priori knowledge required is controllability and observability of the continuous and sampled system and known order.

##### MSC:
 93C40 Adaptive control/observation systems 93C57 Sampled-data control/observation systems
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##### References:
 [1] M. Araki, T. Hagiwara: Pole assignment by multirate sampled data output feedback. Internat. J. Control 44 (1986), 1661-1673. · Zbl 0613.93040 [2] K. G. Arvanitis: Model reference adaptive control of MIMO linear continuous-time systems using multirate generalized sampled-data hold functions. Proc. 2nd IEEE Mediter. Symp. on New Directions in Control and Automation, Chania, Greece 1994, pp. 332-339. [3] K. G. Arvanitis: Adaptive decoupling of linear systems using multirate generalized sampled-data hold functions. IMA J. Math. Control Inform. 12 (1995), 157-177. · Zbl 0832.93033 [4] K. G. Arvanitis: An indirect adaptive pole placer for MIMO systems based on multirate sampling of the plant output. IMA J. Math. Control Inform. 12 (1995), 363-394. · Zbl 0848.93033 [5] K. G. Arvanitis, P. N. Paraskevopoulos: Exact model matching of linear systems using multirate digital controllers. Proc. 2nd E.C.C., Groningen, The Netherlands 1992, vol. 3, pp. 1648-1652. [6] K. G. Arvanitis, P. N. Paraskevopoulos: Sampled-data minimum $$H^\infty$$-norm regulation of continuous-time linear systems using multirate-output controllers. J. Optim. Theory Appl. 87 (1995), 2, 235-267. · Zbl 0841.93041 [7] A. B. Chammas, C. T. Leondes: Pole assignment by piecewise constant output feedback. Internat. J. Control 29 (1979), 31-38. · Zbl 0443.93042 [8] J. P. Greshak, G. C. Vergese: Periodically varying compensation of time-invariant systems. Systems Control Lett. 2 (1982), 88-93. · Zbl 0489.93042 [9] T. Hagiwara, M. Araki: Design of a stable state feedback controller based on the multirate sampling of the plant output. IEEE Trans. Automat. Control AC-33 (1988), 812-819. · Zbl 0648.93043 [10] B. L. Ho, R. E. Kalman: Effective construction of linear state variable models from input/output functions. Regelungstechnik 14 (1966), 545-548. · Zbl 0145.12701 [11] P. T. Kabamba: Control of linear systems using generalised sampled-data hold functions. IEEE Trans. Automat. Control AC-32 (1987), 772-783. · Zbl 0627.93049 [12] P. P. Khargonekar K. Poolla, A. Tannenbaum: Robust control of linear time-invariant plants using periodic compensation. IEEE Trans. Automat. Control AC-30 (1985), 1088-1096. · Zbl 0573.93013 [13] T. Mita B. C. Pang, K. Z. Liu: Design of optimal strongly stable digital control systems and application to output feedback control of mechanical systems. Internat. J. Control 45 (1987), 2071-2082. · Zbl 0616.93051 [14] P. N. Paraskevopoulos, K. G. Arvanitis: Exact model matching of linear systems using generalized sampled-data hold functions. Automatica 30 (1994), 503-506. · Zbl 0800.93329
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