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Abstract

In this paper, we propose a new LMI-based method for robust state-feedback controller synthesis of discrete-time linear periodic/time-invariant systems subject to polytopic uncertainties. In stark contrast with existing approaches that are confined to static controller synthesis, we explore dynamic controller synthesis and reveal a particular periodically timevarying dynamical controller structure that allows LMI-based synthesis. In particular, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based design methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective to achieve less conservative results.

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Abstract

This paper deals with the stability analysis of linear time-delay sys- tems. The time-delay is assumed to be a time-varying C1 function be- longing to an interval and has a bounded derivative. Considering stable delay-free system, the quadratic separation framework is used to assess the maximal allowable value of the delay that preserves stability. To take into account the time-varying nature of the delay, the quadratic separation principle has been extended to cope with the general case of uncertain op- erators (instead of just uncertain matrices). Then, separation conditions lead to linear matrix inequality (LMI) which can be efficiently solved with Semi Definite Programming solvers in Matlab. The paper concludes with an illustrative academic example.

Abstract

Stability analysis of uncertain time-delay systems is considered in a quadratic separation framework. Results are formulated in terms of Linear Matrix Inequalities (LMI) which prove to be conservative. But this conservatism is significantly reduced by combining several tools. Firstly, a fractioning of the delay is performed thus introducing knowledge on the functional defining the current state of the system. Secondly, a Taylor series approximation of the delay operator is performed and the Taylor remainder is explicitly taken into account with a new uncertainty-type approximation. Thanks to LMI formulation, and with the use of slack variables, robustness is guaranteed for all uncertainties and all delays included in some bounded interval which may not include zero.

Abstract

This paper addresses robust stability, H2 performance, and H performance analysis for Linear Time- Invariant Parameter-Dependent (LTIPD) systems, in which the state-space matrices are polynomially parameter-dependent, using polynomially Parameter-Dependent Lyapunov Functions (PDLFs). Our results are derived via multiple slack variable approach, which has previously been proposed for the nonnegativity check of polynomial functions and it has been proved that the conservatism is no more than SOS approach. Our derived conditions are only sufficient conditions for the original problems; however, they encompass the previously proposed methods using single slack variables. We illustrate the effectiveness of our methods with randomly generated numerical examples compared to the methods using single slack variables.

Abstract

The past ten years have witnessed the emergence of many techniques for solving parameter-dependent linear matrix inequality problems relative to robust analysis of dynamical systems. In these, a polynomial parameter-dependent structure of the Lyapunov function is chosen a priori for proving stability and conservative results are proposed to compute the coefficients of the matrix polynomial. Among such results some demonstrate that the polynomial structure of the Lyapunov function is related to an artificially augmented model in descriptor form. These contributions thus justify a renewed interest for robust analysis results in the descriptor context. Linear matrix inequality based formulas are proposed in the quadratic separation framework. Compared with previously derived results they have better numerical behavior, in particular because there is no need for equality constraints and most inequalities are strict.

Abstract

The paper is devoted to design and experimental testing the adaptive identification algorithms of pitch and elevation model parameters for "LAAS Helicopter Benchmark". The adaptive identification algorithms for separate pitch and elevation motions are proposed and the experimental results are presented. Laboratory experiments clarify the properties of the adaptive identification algorithms in real-world conditions.

Abstract

The paper is devoted to design and experimental testing the adaptive algorithms for identification of the angular motion model parameters for "LAAS Helicopter Benchmark". The simplified model describes the iso­lated pitch motion and interrelated elevation and travel motions of the "Helicopter". The adaptive identi­fi­cation algorithms are proposed, and the experimental results are presented. Laboratory experiments clarify the properties of the adaptive identification in the real-world conditions. The identification results may be used to design the 3DOF control laws for the "Helicopter" both for adaptive and non-adaptive cases

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Abstract

Passification-based direct adaptive control is considered for polytopic uncertain linear time-invariant multi-input multi-output systems. Linear Matrix Inequality based results are provided to guarantee that the adaptive algorithm passifies the system whatever the uncertain parameters in some given set. The contributions are based on the introduction of a parallel feed-forward shunt that liberates from the strong equality constraint PB = CTGT often used for strict passification. The shunt, combined with the introduction of slack variables, allows to produce results without assumptions on which data is uncertain in the process model. Formulas pro­ving robust passification are formulated as Linear Matrix Inequality and can therefore be efficiently tested. A simple academic example illustrates the results.

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