Parameter Dependent H∞ Controller Design by Finite Dimensional Lmi Optimization: Application to Trade-Off Dependent Control

Dinh, Marc; Scorletti, Gérard; Fromion, Vincent; Magarotto, Eric

doi:10.3182/20050703-6-cz-1902.01003

Cited by 17 publications

(37 citation statements)

References 10 publications

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“…A parameter-dependent algebraic Riccati equation (PDRE) often arises in the design of controllers such as gain scheduling control (Apkarian et al, 1995), (Stilwell et al, 1999), saturated system control (Megretski, 1996), and trade-off dependent control (Dinh et al, 2003), (Dinh et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

Mixed matrix sign function/DFT inversion method for solving parameter-dependent Riccati equation

Guerra

Yagoubi

Chevrel

2015

Journal of the Franklin Institute

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Section: Introductionmentioning

confidence: 99%

Mixed matrix sign function/DFT inversion method for solving parameter-dependent Riccati equation

Guerra

Yagoubi

Chevrel

2015

Journal of the Franklin Institute

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“…To reduce conservatism in the derivation of the bound, the reasoning relies on a framework based upon explicitly rational parameter dependent Lyapunov functions [28]. Indeed, to achieve our goal, we take benefit of a quadratic D u -stability condition recently introduced in [17], we rewrite it as a parameter-dependent L M I conditions and transform it, using the S-procedure (see [24], [29] and the references therein), into a parameter-independent optimization problem that can be efficiently solved.…”

Section: Introductionmentioning

confidence: 99%

Improved robust D<inf>u</inf>-stability measures via S-procedure

Sari

Bachelier

Mehdi

et al. 2008

2008 American Control Conference

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In this paper we focus on the notion of robust matrix root-clustering analysis in a union of regions that are possibly disjoint and non symmetric. Indeed this work aims at computing a bound on the size of the uncertainty domain preserving matrix D u -stability. A Linear Fractional Transform (LFT) uncertainty is considered. To reduce conservatism, a new approach, based on some generalized S-procedure, is addressed. In the case where the studied matrices depend affinely on the uncertain parameters or when the studied matrices are subject to polytopic uncertainty, it is known that recently developed L M I conditions are effective to assess the robust performance in a less conservative fashion. This paper further extends the preceding results and propose a unified way to obtain new L M I conditions even in the case of rational parameter dependence. Some conservatism induced by some techniques encountered in the literature is here reduced .Index Terms-Robust matrix, D u -stability, S-procedure, L M I .

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“…Following [5], the LMI approach to gain-scheduling relies on converting the underlying control problem into a set of H ∞ control problems parametrized by the scheduling parameter and then converting these problems into an infinite array of LMIs. To overcome the infinite dimensionality of the resulting LMI problem, relaxation techniques are considered [4]; to achieve relaxation of the LMIs to a finite dimensional problem, an LFT dependency structure of the system on the scheduling parameters [6], polynomial representations [7] or rational approximations [8] are often needed. The technical assumption of convexity of the set of models is another essential requirement of this approach [6], [7], [9], which may result in more conservative performance.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike the mentioned references using the direct LMI approach, the scheduling algorithm developed in [10] uses the interpolation approach to gainscheduling originated from [11]. This approach has an advantage that the scheduling parameters are not required to be polytopic/polynomial/rational dependent; this allows to avoid the restrictions in [6], [7], [8], [9], e.g., overbounding of the underlying set of system models by a convex set.…”

Section: Introductionmentioning

confidence: 99%

Robust stabilization of LPV systems with structured uncertainty using minimax controllers

Ugrinovskii

2007

2007 46th IEEE Conference on Decision and Control

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Abstract-This paper addresses a robust control scheduling scheme for uncertain linear parameter-varying systems with structured uncertainty. A gain-scheduled controller is proposed which employs a set of minimax optimal robust controllers and incorporates an interpolation rule to achieve continuity of the controller gain over a range of operating conditions. Novel weighted time-domain integral quadratic constraints are introduced to assist in the derivation of the controller. The key idea of the interpolation for the structured uncertainty case is to transform the parameterized algebraic Riccati inequalities into equivalent linear matrix inequalities. For every fixed value of the system parameter, the proposed controller guarantees robust stability and a certain bound on the worst-case performance of the corresponding uncertain closed loop system. Furthermore, a bound on the rate of parameter variations is obtained under which the closed loop LPV system is robustly stable. To obtain the proposed controller, a set of semi-definite programming problems are introduced; this enables an efficient numerical solution to the problem under consideration.

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Parameter Dependent H∞ Controller Design by Finite Dimensional Lmi Optimization: Application to Trade-Off Dependent Control

Cited by 17 publications

References 10 publications

Mixed matrix sign function/DFT inversion method for solving parameter-dependent Riccati equation

Mixed matrix sign function/DFT inversion method for solving parameter-dependent Riccati equation

Improved robust D<inf>u</inf>-stability measures via S-procedure

Robust stabilization of LPV systems with structured uncertainty using minimax controllers

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