Gain-Scheduled Control Synthesis Using Dynamic $D$-Scales

Scherer,; Kose,

doi:10.1109/tac.2012.2184609

Cited by 37 publications

(7 citation statements)

References 27 publications

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“…Since M , N enter (8), (9) and (15) affinely, we can verify feasibility of (8)- (10) and (15) in the variables X, Y, Z and M, N . If solutions exist, one can construct an LPV controller for which K has McMillan degree n+n Ψ , while the number of repetitions of δ in the controller is c = p + n Ψ (because the dimension of Ψ e in the proof of Theorem 3 is p+n Ψ +p).…”

Section: Is Guaranteed Ifmentioning

confidence: 99%

“…Theorem 3: There exists a controller K (as in Fig. 3) which internally stabilizes G and some Ψ e ∈ RL (p+c)×(p+c) ∞ with (12) iff there exist transfer matrices (14) in RL p×p ∞ such that the LMIs (8)- (10) and (15) are feasible.…”

Section: Is Guaranteed Ifmentioning

confidence: 99%

“…In the specialization of Theorem 3 to static multipliers (n Ψ = 0), this coupling is not present any more, while also (10) reduces to the standard relation between X 22 and Y 22 . • Gain-scheduling control by dynamic D-scalings has been addressed in [15], [16]. The generalization derived in this paper is considerably simpler.…”

Section: Is Guaranteed Ifmentioning

confidence: 99%

“…For arbitrary fast variations, the constant D-scaling problem has been addressed in [11], [12], while a reduction of conservatism has been in achieved in [13], [14] by using constant D/Gscalings. The respective problem for dynamic multipliers was completely open until we managed to find an LMI solution to the gain-scheduling problem by dynamic D-scalings rather recently [15], [16]. (See also [17], [18] for a non-convex solution.)…”

Section: Introductionmentioning

confidence: 99%

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Gain-scheduled synthesis with dynamic positive real multipliers

Scherer

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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If designing robust controllers based on multiplier or separation techniques, one is confronted with weighting filters that are not necessarily stable. For optimal synthesis, this requires controllers to be only partially internally stabilizing. In this paper we propose a new synthesis framework for possibly unstable performance weights. It is further shown how these results can be used to design gain-scheduling controllers with dynamic positive real multipliers by convex optimization, a problem without any analogous solution in the literature.

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Section: Is Guaranteed Ifmentioning

confidence: 99%

Section: Is Guaranteed Ifmentioning

confidence: 99%

Section: Is Guaranteed Ifmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Gain-scheduled synthesis with dynamic positive real multipliers

Scherer

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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“…Many results have been obtained in this respect; see e.g. [12][13][14][15][16][17][18][19]2] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and control of a class of LPV systems with piecewise constant parameters

Briat

2015

Systems & Control Letters

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Observer‐based linear parameter‐varying control with guaranteed ‐gain and ‐type performance objectives

Köroğlu

2013

Intl J Robust & Nonlinear

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SUMMARY Synthesis of an observer‐based linear parameter‐varying controller is considered for a general linear parameter‐varying plant. The parameter vector and its derivative are both assumed to take values in known bounded domains, whereas only the parameter vector is assumed to be measurable during online operation. The synthesis problem is considered for scriptL2‐gain and scriptH2‐type performance objectives. Potentially conservative parameter‐dependent linear matrix inequality conditions are derived for the solvability of these two problems. To facilitate the reduction of conservatism, the conditions are expressed in a way to have bilinear dependence on an arbitrary positive scalar. In addition to employing a suitable relaxation scheme to reduce these conditions into finitely many constraints, a line search hence needs to be performed over the positive scalar to obtain the best achievable performance with an observer‐based controller. The online implementation of the observer‐based controller is relatively simpler if compared with a controller of unrestricted structure. Moreover, the observer‐based controller will have no dependence on the parameter derivatives irrespective of the choices of the design variables. Copyright © 2013 John Wiley & Sons, Ltd.

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Gain-Scheduled Control Synthesis Using Dynamic $D$-Scales

Cited by 37 publications

References 27 publications

Gain-scheduled synthesis with dynamic positive real multipliers

Gain-scheduled synthesis with dynamic positive real multipliers

Stability analysis and control of a class of LPV systems with piecewise constant parameters

Observer‐based linear parameter‐varying control with guaranteed ‐gain and ‐type performance objectives

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