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Robust Adaptive Stabilization of Linear Time-Invariant Dynamic Systems by Using Fractional-Order Holds and Multirate Sampling Controls

  • De la Sen Parte, Manuel
  • Alonso Quesada, Santiago
Es reproducción del documento publicado en http://dx.doi.org/10.1155/2010/620546, 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., Ministerio de Ciencia y Tecnologia DPI2006-00714 y DPI 2009-07197
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About the stability and positivity of a class of discrete nonlinear systems of difference equations

  • De la Sen Parte, Manuel
Es reproducción del documento publicado en http://dx.doi.org/10.1155/2008/595367, This paper investigates stability conditions and positivity of the solutions of a coupled set of nonlinear difference equations under very generic conditions of the nonlinear real functions which are assumed to be bounded from below and nondecreasing. Furthermore, they are assumed to be linearly upper bounded for sufficiently large values of their arguments. These hypotheses have been stated in 2007 to study the conditions permanence.
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Model-matching-based control of the Beverton-Holt equation in Ecology

  • De la Sen Parte, Manuel
  • Alonso Quesada, Santiago
Es reproducción del documento publicado en http://dx.doi.org/10.1155/2008/793512, Beverton-Holt equation of Ecology has a prescribed solution. The way used to achieve the tracking objective is the design of a carrying capacity through a feedback law so that the prescribed reference sequence, which defines the suitable behavior, is achieved. The advantage that the inverse of the Beverton-Holt equation is a linear time-varying discrete dynamic system whose external input is the inverse of the environment carrying capacity is taken in mind. In the case when the intrinsic growth rate is not perfectly known, an adaptive law implying parametrical estimation is incorporated to the scheme so that the tracking property of the reference sequence becomes an asymptotic objective in the absence of additive disturbances. The main advantage of the proposal is that the population evolution might behave as a prescribed one either for all time or asymptotically, which defines the desired population evolution. The technique might be of interest in some industrial exploitation problems like, for instance, in aquaculture management.
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Adaptive control of single-input single-output hybrid systems possessing interacting discrete- and continuous-time dynamics

  • De la Sen Parte, Manuel
Es reproducción del documento publicado en http://dx.doi.org/10.1155/DDNS.2005.299, This paper deals with the problem of synthesizing a robust adaptive controller for a specific class of single-input single-output (SISO) time-invariant hybrid controlled object (plant) which can operate under bounded disturbances and/or unmodeled dynamics. The hybrid plant dealt with is composed of two coupled subsystems, one of them being of continuous-time type while the other is digital. As a result there are also mixed continuous-time and discrete signals present in the system associated either with the solutions of differential equations which depend at the same time on both discrete-time and continuous-time forcing terms and on generalized difference equations associated with discretized and digital signals. The estimation algorithm is of a continuous-time nature since the plant parameter estimates are updated for all time. It also incorporates a relative adaptation dead-zone as a robust stabilization mechanism which prevents against instability in the presence of a common class of unmodeled dynamics and bounded noise.
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Stability Results for Switched Linear Systems with Constant Discrete Delays

  • De la Sen Parte, Manuel
  • Ibeas Hernández, Asier
Es reproducción del documento publicado en http://dx.doi.org/10.1155/2008/543145, This paper investigates the stability properties of switched systems possessing several parameterizations (or configurations) while being subject to internal constant point delays. Some of the stability results are formulated based on Gronwall's lemma for global exponential stability, and they are either dependent on or independent of the delay size but they depend on the switching law through the requirement of a minimum residence time. Another set of results concerned with the weaker property of global asymptotic stability is also obtained as being independent of the switching law, but still either dependent on or independent of the delay size, since they are based on the existence of a common Krasovsky-Lyapunov functional for all the above-mentioned configurations. Extensions to a class of polytopic systems and to a class of regular time-varying systems are also discussed., Ministerio de Educación DPI2006-00714 y GIC07143-IT-269-07 ; Gobierno Vasco SAIOTEK SPED06UN10 y SPE07UN04
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Stability Results of a Class of Hybrid Systems under Switched Continuous-Time and Discrete-Time Control

  • De la Sen Parte, Manuel
  • Ibeas Hernández, Asier
Es reproducción del documento publicado en http://dx.doi.org/10.1155/2009/315713, This paper investigates the stability properties of a class of switched systems possessing several linear time-invariant parameterizations (or configurations) which are governed by a switching law. It is assumed that the parameterizations are stabilized individually via an appropriate linear state or output feedback stabilizing controller whose existence is first discussed. A main novelty with respect to previous research is that the various individual parameterizations might be continuous-time, discrete-time, or mixed so that the whole switched system is a hybrid continuous/discrete dynamic system. The switching rule governs the choice of the parameterization which is active at each time interval in the switched system. Global asymptotic stability of the switched system is guaranteed for the case when a common Lyapunov function exists for all the individual parameterizations and the sampling period of the eventual discretized parameterizations taking part of the switched system is small enough. Some extensions are also investigated for controlled systems under decentralized or mixed centralized/decentralized control laws which stabilize each individual active parameterization., Spanish Ministry of Education by its support of this work through Grant DPI2006-00714. They also thank the Basque Government for its support through GIC07143-IT-269-07, SAIOTEK SPED06UN10, and SPE07UN04
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On the properties of reachability, observability, controllability, and constructibility of discrete-time positive time-invariant linear systems with aperiodic choice of the sampling instants

  • De la Sen Parte, Manuel
Es reproducción del documento publicado en http://dx.doi.org/10.1155/2007/84913, This paper investigates the properties of reachability, observability, controllability, and constructibility of positive discrete-time linear time-invariant dynamic systems when the sampling instants are chosen aperiodically. Reachability and observability hold if and only if a relevant matrix defining each of those properties is monomial for the set of chosen sampling instants provided that the continuous-time system is positive. Controllability and constructibility hold globally only asymptotically under close conditions to the above ones guaranteeing reachability/observability provided that the matrix of dynamics of the continuous-time system, required to be a Metzler matrix for the system's positivity, is furthermore a stability matrix while they hold in finite time only for regions excluding the zero vector of the first orthant of the state space or output space, respectively. Some related properties can be deduced for continuous-time systems and for piecewise constant discrete-time ones from the above general framework.
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About Robust Stability of Dynamic Systems with Time Delays through Fixed Point Theory

  • De la Sen Parte, Manuel
This paper investigates the global asymptotic stability independent of the sizes of the delays of linear time-varying systems with internal point delays which possess a limiting equation via fixed point theory. The error equation between the solutions of the limiting equation and that of the current one is considered as a perturbation equation in the fixed-point and stability analyses. The existence of a unique fixed point which is later proved to be an asymptotically stable equilibrium point is investigated. The stability conditions are basically concerned with the matrix measure of the delay-free matrix of dynamics to be negative and to have a modulus larger than the contribution of the error dynamics with respect to the limiting one. Alternative conditions are obtained concerned with the matrix dynamics for zero delay to be negative and to have a modulus larger than an appropriate contributions of the error dynamics of the current dynamics with respect to the limiting one. Since global stability is guaranteed under some deviation of the current solution related to the limiting one, which is considered as nominal, the stability is robust against such errors for certain tolerance margins, Ministerio de Educación (DPI2006-00714); Gobierno Vasco (GIC07143-IT-269-07, SAIOTEK SPED06UN10, SPE07UN04)
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On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays

  • De la Sen Parte, Manuel
  • Ibeas Hernández, Asier
Es reproducción del documento publicado en http://dx.doi.org/10.1155/2008/231710, This paper investigates the asymptotic stability of switched linear time-varying systems with constant point delays under not very stringent conditions on the matrix functions of parameters. Such conditions are their boundedness, the existence of bounded time derivatives almost everywhere, and small amplitudes of the appearing Dirac impulses where such derivatives do not exist. It is also assumed that the system matrix for zero delay is stable with some prescribed stability abscissa for all time in order to obtain sufficiency-type conditions of asymptotic stability dependent on the delay sizes. Alternatively, it is assumed that the auxiliary system matrix defined for all the delayed system matrices being zero is stable with prescribed stability abscissa for all time to obtain results for global asymptotic stability independent of the delays. A particular subset of the switching instants is the so-called set of reset instants where switching leads to the parameterization to reset to a value within a prescribed set, Ministerio de Educación (DPI2006-00714); Gobierno Vasco (GIC07143-IT-269-07;SAIOTEK SPED06UN10 y SPE07UN04)
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Risk factors for dementia in the epidemiological study of Munguialde County (Basque Country-Spain)

  • Fernández Martínez, Manuel
  • Castro Flores, Jessica
  • Pérez de las Heras, Susana
  • Mandaluniz Lekumberri, Aitziber
  • Gordejuela Menocal, María
  • Zarranz Imirizaldu, Juan José
Es reproducción del documento publicado en http://dx.doi.org/10.1186/1471-2377-8-39, Background: Prevalence of degenerative dementias and dementias associated with cerebrovascular disease is increasing. Dementia is one of the most significant public health problem. In recent years, the role of vascular risk factors (hypertension, diabetes mellitus and hypercholesterolemia) and depression has been evaluated. The incidence of dementia and risk factors has not been fully investigated in Spain. The aim of this study was to identify the risk factors for dementia, Alzheimer's disease (AD) and vascular dementia (VD) in elderly people in Munguialde County (Spain). Methods: A two phase, door-to-door populational study was performed. Demographic variables and the presence of vascular risk factors and depression were recorded. The MMSE, the DSM-IV and the conventional criteria for AD and VD were used in the evaluation. The odds ratio for each risk factor was calculated by logistic regression analysis. Results: 1756 healthy subjects and 175 patients with dementia participated in the study. Of these, 133 had AD, 15 VD and the remainder other dementias. The risk factors for dementia and AD were female sex (OR = 1.67 and 1.97, respectively); age (OR = 1.14 and 1.15); stroke (OR = 7.84 and 3); and depression (OR = 53.08 and 3.19). Stroke was the only risk factor for VD (OR = 119). Conclusion: Greater age, female sex, stroke and depression increase the risk of suffering dementia, AD and VD. The relationship between depression, vascular risk factors and dementia has clear public health implications. Prevention and early treatment of vascular risk factors and depression may have an important impact in lowering the risk of dementia and could modify the natural history of the disease., Fundación San Jose Etxealai; Fundación BBK
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