Parametric Lyapunov function approach to H2 analysis and control of linear parameter-dependent systems

Souza, Carlos E. de; Trofino, Alexandre; Oliveira, José de

doi:10.1049/ip-cta:20030709

Cited by 44 publications

(34 citation statements)

References 20 publications

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“…Assuming that the closed-loop system (7) is exponentially stable, one has that, for all possible trajectories of α(t), the associated H 2 norm defined as [35] …”

Section: Robust H 2 Controlmentioning

confidence: 99%

Robust ℋ2 control applied to boost converters: design, experimental validation and performance analysis

Maccari

Montagner

Pinheiro

et al. 2012

IET Control Theory &Amp; Applications

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This study proposes a design procedure and experimental validation for a robust H 2 state feedback controller applied to a DC-DC boost converter modelled as a linear system affected by time-varying parameters lying in known intervals. The parameters considered as time-varying are the input voltage, the load resistance and the operating point duty cycle. A polytopic representation of the system is derived and the controller is designed by means of a convex optimisation problem based on linear matrix inequalities. The conventional H 2 controller is extended to cope with alpha-stability and robust linear quadratic regulator design, providing different strategies to trade-off the magnitude of the control gains and the response of the closed-loop system. Tight correspondences between numerical simulations and the experimental results prove the viability of the application of this technique for this kind of plant. Finally, a robust performance analysis illustrates the capacity of the closed-loop system to reject energy bounded disturbances, with interpretation for the cases of time-varying and time-invariant parameters.

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“…Assuming that the closed-loop system (7) is exponentially stable, one has that, for all possible trajectories of α(t), the associated H 2 norm defined as [35] …”

Section: Robust H 2 Controlmentioning

confidence: 99%

Robust ℋ2 control applied to boost converters: design, experimental validation and performance analysis

Maccari

Montagner

Pinheiro

et al. 2012

IET Control Theory &Amp; Applications

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“…(1)-(2) (the reader can see [1][2][3][4][5][6] for different kind of problems). Such simplification may, however, yield unnecessarily conservative control systems or even result in unstable ones: at very least, parameter variation rates must also be included in the design, as in [7,8] or [9]. Some LPV control system designs modify linear matrix inequalities-based (LMIbased) methods to incorporate conditions such as maximum parameter variation rates, like [10] or [11].…”

Section: Introductionmentioning

confidence: 98%

Parameter estimation on linear time-varying systems

Souza

Palhares

2011

Journal of the Franklin Institute

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“…This is different from [20] because it does not use weighting transfer functions; from [74] because the matrices obtained for different values of the uncertainty are not set to zero, but assume constant values; from [63] where the uncertainty is expressed as a hypersphere; from [278,[280][281][282] in that the proposed method copes with the general case of uncertain matrices while the works by Sato and coworkers consider only the case of uncertain scheduling parameters. It is also different from [188] in not assuming a stochastic description of the parameter uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…Since the bounds on the derivatives of the scheduling parameters are explicitly taken into account, the approach proposed in [105] provides a smooth transition between time invariant parameters and arbitrarily fast parameter variations. Further development of this approach can be found in [354], where H ∞ control synthesis was considered, in [74], where H 2 control synthesis was considered, and in [72], where an extended characterization of H 2 and H ∞ norms was provided, allowing to further decrease the conservatism when using parameter-dependent Lyapunov functions. Homogeneous polynomially parameter-dependent quadratic Lyapunov functions were proposed by [54], demonstrating their effectiveness with respect to linearly parameterdependent Lyapunov functions.…”

Section: Analysis Based On Other Lyapunov Functionsmentioning

confidence: 99%

“…However, the design of controllers for LPV systems has been usually performed under the assumption that there was no model uncertainty. Only a few papers have stated the importance of considering robustness against uncertainty [3,15,16,20,33,74,229,309,315,352]. In recent years, works dealing with inexactly measured parameters have been an important field of research.…”

Section: Introductionmentioning

confidence: 99%

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Advances in Gain-Scheduling and Fault Tolerant Control Techniques

Rotondo¹

2018

Springer Theses

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This thesis presents some contributions to the state-of-the-art of the fields of gainscheduling and fault tolerant control (FTC).In the area of gain-scheduling, the connections between the linear parameter varying (LPV) and Takagi-Sugeno (TS) paradigms are analyzed, showing that the methods for the automated generation of models by nonlinear embedding and by sector nonlinearity, developed for one class of systems, can be easily extended to deal with the other class. Then, two measures, based on the notions of overboundedness and region of attraction estimates, are proposed in order to compare different models and choose which one can be considered the best one. Later, the problem of designing state-feedback controllers for LPV systems has been considered, providing two main contributions. First, robust LPV controllers that can guarantee some desired performances when applied to uncertain LPV systems are designed, by using a double-layer polytopic description that takes into account both the variability due to the varying parameter vector and the uncertainty. Then, the idea of designing the controller in such a way that the required performances are scheduled by the varying parameters is explored, which provides an elegant way to vary online the behavior of the closed-loop system. In both cases, the problem reduces to finding a solution to a finite number of linear matrix inequalities (LMIs), which can be done efficiently using the available solvers.In the area of fault tolerant control, the thesis first shows that the aforementioned double-layer polytopic framework can be used for FTC, in such a way that different strategies (passive, active and hybrid) are obtained depending on the amount of available information. Later, an FTC strategy for LPV systems that involves a reconfigured reference model and virtual actuators is developed. It is shown that by including the saturations in the reference model equations, it is possible to design a model reference FTC system that automatically retunes the reference states whenever the system is affected by saturation nonlinearities. In this way, a graceful performance degradation in presence of actuator saturations is incorporated in an elegant way. Finally, the problem of FTC of unstable LPV systems subject to actuator saturations is considered. In this case, the design of the virtual actuator is performed in such a way that the convergence of the state trajectory to zero is assured despite the saturations and the appearance of faults. Also, it is shown that it is possible to obtain some guarantees about the tolerated delay between the fault occurrence and its isolation, and that the nominal controller can be designed so as to maximize the tolerated delay.i Resum Aquesta tesi presenta diverses contribucions a l'estat de l'art del control per planificació del guany i del control tolerant a fallades (FTC).Pel que fa al control per planificació del guany, s'analitzen les connexions entre els paradigmes dels sistemes lineals a paràmetres variants en el temps (LPV) i d...

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Parametric Lyapunov function approach to H2 analysis and control of linear parameter-dependent systems

Cited by 44 publications

References 20 publications

Robust ℋ2 control applied to boost converters: design, experimental validation and performance analysis

Robust ℋ2 control applied to boost converters: design, experimental validation and performance analysis

Parameter estimation on linear time-varying systems

Advances in Gain-Scheduling and Fault Tolerant Control Techniques

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