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A loopedfunctional approach for robust stability analysis of linear impulsive systems
 Systems & Control Letters
, 2012
"... Abstract A new functionalbased approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces loopedfunctionals, considers nonmonotonic Lyapunov functions and leads to LMIs conditions devoid of exponential terms. This allows one to easily formulate ..."
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Cited by 9 (5 self)
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Abstract A new functionalbased approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces loopedfunctionals, considers nonmonotonic Lyapunov functions and leads to LMIs conditions devoid of exponential terms. This allows one to easily formulate dwelltimes results, for both certain and uncertain systems. It is also shown that this approach may be applied to a wider class of impulsive systems than existing methods. Some examples, notably on sampleddata systems, illustrate the efficiency of the approach.
ModelBased Networked Control Systems: Stability
, 2002
"... In this report the control of continuous linear plants where the state sensor is connected to a linear controller/actuator via a network is addressed. The work focuses on reducing the network usage using knowledge of the plant dynamics. Specifically, the controller uses an explicit model of the plan ..."
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Cited by 6 (3 self)
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In this report the control of continuous linear plants where the state sensor is connected to a linear controller/actuator via a network is addressed. The work focuses on reducing the network usage using knowledge of the plant dynamics. Specifically, the controller uses an explicit model of the plant that approximates the plant dynamics and makes possible stabilization of the plant even under slow network conditions. Necessary and sufficient conditions for stability are derived for the presented setup in terms of the update time h and the parameters of the plant and of its model. The deterioration of behavior when either h or the modeling error increase is explicitly shown.
Robust stability of impulsive systems: A functionalbased approach
 in "4th IFAC conference on Analysis and Design of Hybrid Systems (ADHS’2012
, 2012
"... Abstract: An improved functionalbased approach for the stability analysis of linear uncertain impulsive systems relying on Lyapunov loopedfunctionals is provided. Looped functionals are peculiar functionals that allow to encode discretetime stability criteria into continuoustime conditions and t ..."
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Cited by 5 (3 self)
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Abstract: An improved functionalbased approach for the stability analysis of linear uncertain impulsive systems relying on Lyapunov loopedfunctionals is provided. Looped functionals are peculiar functionals that allow to encode discretetime stability criteria into continuoustime conditions and to consider nonmonotonic Lyapunov functions along the trajectories of the impulsive system. Unlike usual discretetime stability conditions, the obtained ones are convex in the system matrices, an important feature for extending the results to uncertain systems. It is emphasized in the examples that the proposed approach can be applied to a class of systems for which existing approaches are inconclusive, notably systems having unstable continuous and discrete dynamics.
Robustness Analysis for the Certification of Digital Controller Implementations ∗ ABSTRACT
"... Despite recent advances in the field of Networked Control Systems (NCS), the gap between the control design stage and the implementation stage on a physical platform remains significant. The simplifying assumptions made in the analysis of NCS are often not precise enough for realistic embedded contr ..."
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Despite recent advances in the field of Networked Control Systems (NCS), the gap between the control design stage and the implementation stage on a physical platform remains significant. The simplifying assumptions made in the analysis of NCS are often not precise enough for realistic embedded control systems, and engineers must resort to timeconsuming simulations and multiple redesign and testing phases before the performance of a system is judged adequate. Moreover, simulationbased methods do not typically provide rigorous performance or stability guarantees. We approach the problem of certifying a digital controller implementation from an inputoutput, robust control perspective. Following a standard method for analyzing sampleddata systems, we view the implementation step as a perturbation of a nominal linear timeinvariant model. Nonlinearities
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"... Multirate trackfollowing control with robust stability for a dualstage multisensing servo system in HDDs ..."
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Multirate trackfollowing control with robust stability for a dualstage multisensing servo system in HDDs
Computation of lower bounds for the induced L2 norm of LPV systems
"... Determining the induced L2 norm of a linear, parametervarying (LPV) system is an integral part of many analysis and robust control design procedures. Most prior work has focused on efficiently computing upper bounds for the induced L2 norm. The conditions for upper bounds are typically based on sca ..."
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Determining the induced L2 norm of a linear, parametervarying (LPV) system is an integral part of many analysis and robust control design procedures. Most prior work has focused on efficiently computing upper bounds for the induced L2 norm. The conditions for upper bounds are typically based on scaled smallgain theorems with dynamic multipliers or dissipation inequalities with parameter dependent Lyapunov functions. This paper presents a complementary algorithm to compute lower bounds for the induced L2 norm. The proposed approach computes a lower bound on the gain by restricting the parameter trajectory to be a periodic signal. This restriction enables the use of recent results for exact calculation of the L2 norm for a periodic linear time varying system. The proposed lower bound algorithm returns also a worstcase parameter trajectory for the LPV system that can be further analyzed to provide insight into the system performance.
1Algebraic Characterisation of the H ∞ and H2 Norms for Linear ContinuousTime Periodic Systems∗
"... It is wellknown that linear, periodically timevarying, continuoustime systems are formally equivalent to socalled lifted representations that are shiftinvariant, but have spatially infinitedimensional inputs and outputs. By shift invariance, corresponding frequencydomain representations can ..."
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It is wellknown that linear, periodically timevarying, continuoustime systems are formally equivalent to socalled lifted representations that are shiftinvariant, but have spatially infinitedimensional inputs and outputs. By shift invariance, corresponding frequencydomain representations can be constructed. Indeed, it makes sense to use the H ∞ norm of the associated frequencydomain symbol as a measure of system size. In fact, this is equal to the L2[0,∞) induced norm of the system. As an alternative measure of system size a generalisation of the H2 norm, which characterises the impulsive response of the system, can also be defined. The purpose of this paper is to establish finitedimensional, algebraic characterisations of these norms, for linear continuoustime periodic systems. 1