An IQC-based stability criterion for systems with slowly varying parameters

2008 47th IEEE Conference on Decision and Control

2008

Abstract-In this paper the design of robust H2-estimators for the class of linear systems that depend rationally on ratebounded uncertain time-varying parameters is addressed. The uncertainties are characterized by dynamic IQCs and new LMI conditions are formulated that allow for a nontrivial extension of the estimation problem with a weighting filter at the output. In order to show the power of the dynamic IQC approach, a numerical example is included in which the result is compared with alternative approaches based on parameter-dependent Lyapunov functions. The effectiveness of the additional weighting filter is illustrated in a second numerical example.

“…It is now possible to arrive at the following test from [13], which basically is a reformulation of the test from [12].…”

Section: Robust Stability and H 2 -Performance For Ltv-systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An IQC approach to robust estimation against perturbations of smoothly time-varying parameters

Veenman

Köroğlu

2008 47th IEEE Conference on Decision and Control

2008

“…[16]). The IQC tests developed by [9], [10] for robust stability analysis against time-varying parameters, rely on the swapping lemma for time-varying multiplication operators. In the following parts of this section, we proceed along the line of the extension approach due to [10], to provide an IQC test that we will make use of in developing robust stability analysis methods for various ROVs.…”

Section: An Iqc Test For Robust Stability Analysis Against Time-vmentioning

confidence: 99%

“…Research within robust control theory has provided, in the form of feasibility tests, a variety of techniques for robust stability analysis against perturbations of smoothly timevarying parameters, based on parameter-dependent Lyapunov function approach [1], [2], [3], [4], [5], multiplier theory [6], [7] or integral quadratic constraints (IQC) theorem [8], [9], [10], [11], [12], [13].…”

Section: Introductionmentioning

confidence: 99%

“…Contrary to [6], [7], we consider a broad class of regions, thus allowing for different types of variations for the parameters. Along the lines of our previous work [13] that generalized the IQC approach of [10], we then state in Section IV an IQC theorem based on the so-called swapping lemma. This theorem allows us to derive robust stability analysis tests for polytopic ROVs and ROVs described by matrix inequalities in Section V and Section VI respectively.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Stability Analysis against Perturbations of Smoothly Time-Varying Parameters

Köroğlu

Proceedings of the 45th IEEE Conference on Decision and Control

2006

Robust stability analysis problem is considered for linear time-invariant systems subject to perturbations of parameters that vary smoothly in time. The problem is formulated by describing the uncertainty in the form of a regionof-variation that covers all possible trajectories obtained by plotting the variation of the parameter at a certain time versus the parameter itself at that same instant of time. In this fashion, the possible and very probable correlation between the parameter and its variation is taken into account. The problem is elaborated on via an integral quadratic constraints approach and, based on a main result relying on the swapping lemma, robust stability analysis tests are derived for polytopic regions of variation as well as for regions with generic descriptions expressed in terms of matrix inequalities. The tests for polytopic regions-of-variation are based on the convex hull and Pólya relaxation approaches, whereas the test for general regions relies on the sum-of-squares relaxation approach. The new tests offer significant reduction in conservatism at the cost of extra computational complexity.

Robust output feedback control against disturbance filter uncertainty described by dynamic integral quadratic constraints

Dietz¹,

Intl J Robust & Nonlinear

2009

SUMMARYMotivated by a robust disturbance rejection problem, in which disturbances are described by an uncertain filter at the plant input, a convex solution is presented for the robust output feedback controller synthesis problem for a particularly structured plant. The uncertainties are characterized by an integral quadratic constraint (IQC) with general frequency-dependent multipliers. By exploiting the structure of the generalized plant, linear matrix inequality (LMI)-synthesis conditions are derived in order to guarantee a specified L 2 -gain or H 2 -norm performance level, provided that the IQC multipliers are described by LMI constraints. Moreover, it is shown that part of the controller variables can be eliminated. Finally, the rejection of non-stationary sinusoidal disturbance signals is considered. In a numerical example, it is shown that specifying a bound on the rate-of-variation of the time-varying frequency can improve the performance if compared with the static IQC multipliers.