Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume 2010, Article ID 620546, 27 pages doi:10.1155/2010/620546 Research Article Robust Adaptive Stabilization of Linear Time-Invariant Dynamic Systems by Using Fractional-Order Holds and Multirate Sampling Controls S. Alonso-Quesada and M. De la Sen Department of Electricity and Electronics, Faculty of Science and Technology, University of Basque Country, Leioa 48940, Spain Correspondence should be addressed to S. Alonso-Quesada, santi@we.lc.ehu.es Received 8 June 2009; Accepted 2 February 2010 Academic Editor: Francisco Solis Copyright q 2010 S. Alonso-Quesada and M. De la Sen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper presents a strategy for designing a robust discrete-time adaptive controller for stabilizing linear time-invariant LTI continuous-time dynamic systems. Such systems may be unstable and noninversely stable in the worst case. A reduced-order model is considered to design the adaptive controller. The control design is based on the discretization of the system with the use of a multirate sampling device with fast-sampled control signal. A suitable on-line adaptation of the multirate gains guarantees the stability of the inverse of the discretized estimated model, which is used to parameterize the adaptive controller. A dead zone is included in the parameters estimation algorithm for robustness purposes under the presence of unmodeled dynamics in the controlled dynamic system. The adaptive controller guarantees the boundedness of the system measured signal for all time. Some examples illustrate the efficacy of this control strategy. 1. Introduction Adaptive control theory has been widely applied for stabilizing increasingly complex engineering systems with large uncertainties 1, including the incorporation of parallel multiestimation and time-delayed and hybrid models 2–6. Such model uncertainties may come from the fact that the parameters of the dynamic system model are partially or fully unknown and/or from the presence of unmodeled dynamics 3. On the other hand, discrete equations are useful for modeling and controlling discretized continuous-time systems in practical situations 2, 5–9 and as a tool for describing more complex nonlinear structures via discretization 10, 11. A frequently used method to stabilize an unknown dynamic system is