Characterization and Computation of $\mathcal{H}_{\infty}$ Norms for Time-Delay Systems

Michiels, Wim; Gümüşsoy, Suat

doi:10.1137/090758751

Cited by 26 publications

(46 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to compute γ H for p = 2, we use the software HINFN [14]. However, HINFN is not able to handle delayed states in the output (see H RR and H T OD ).…”

Section: Batch Reactor Case Studymentioning

confidence: 99%

Stabilizing transmission intervals and delays for nonlinear Networked Control Systems: The large delay case

Tolić

Hirche

2014

53rd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

This paper proposes a methodology for computing Maximally Allowable Transfer Intervals (MATIs) that provably stabilize nonlinear Networked Control Systems (NCSs) in the presence of disturbances and signal delays. Accordingly, given a desired level of system performance (in terms of Lpgains), quantitative MATI vs. delay trade-offs are obtained. By combining impulsive delayed system modeling with LyapunovRazumikhin type of arguments, we are able to consider even the so-called large delays. Namely, the computed MATIs can be smaller than delays existent in NCSs. In addition, our stability results are provided for the class of Uniformly Globally Exponentially Stable (UGES) scheduling protocols. The wellknown Round Robin (RR) and Transmit-Once-Discard (TOD) protocols are examples of UGES protocols. Apart from the inclusion of large delays, another salient feature of our methodology is the consideration of corrupted data. To that end, we propose the notion of Lp-stability with bias. Furthermore, the Zeno-free property of our methodology is demonstrated. Finally, a comparison with the state-of-the-art work is provided utilizing the benchmark problem of batch reactor.

show abstract

“…In order to compute γ H for p = 2, we use the software HINFN [14]. However, HINFN is not able to handle delayed states in the output (see H RR and H T OD ).…”

Section: Batch Reactor Case Studymentioning

confidence: 99%

Stabilizing transmission intervals and delays for nonlinear Networked Control Systems: The large delay case

Tolić

Hirche

2014

53rd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

show abstract

“…The H ∞ norm of T , as defined by (10), is 2.6422 and the strong H ∞ norm of the corresponding asymptotic transfer function T a is 4. From property (14), we conclude that the strong H ∞ norm of T (10) is 4.…”

Section: The Strong H-infinity Norm Of Time-delay Systemsmentioning

confidence: 91%

Tuning an H-Infinity Controller with a Given Order and a Structure for Interconnected Systems with Delays

Gümüşsoy

Michiels

2014

Low-Complexity Controllers for Time-Delay Systems

Self Cite

View full text Add to dashboard Cite

An eigenvalue based framework is developed for the H ∞ norm analysis and its norm minimization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations (DDAEs). For these equations H ∞ norms are analyzed and their sensitivity with respect to small delay perturbations is studied. Subsequently, numerical methods for the H ∞ norm computation and for designing controllers minimizing the H ∞ norm with a prescribed structure or order, based on a direct optimization approach, are briefly addressed. The effectiveness of the approach is illustrated with a software demo. The chapter concludes by pointing out the similarities with the computation and optimization of characteristic roots of DDAEs. IntroductionIn many control applications, robust controllers are desired to achieve stability and performance requirements under model uncertainties and exogenous disturbances [22]. The design requirements are usually defined in terms of H ∞ norms of closedloop transfer functions including the plant, the controller and weights for uncertainties and disturbances. There are robust control methods to design the optimal H ∞ controller for linear finite dimensional multi-input-multi-output (MIMO) systems based on Riccati equations and linear matrix inequalities (LMIs), see e.g. [5,7] and the references therein. The order of the controller designed by these methods is typically larger or equal to the order of the plant. This is a restrictive condition for high-S. Gumussoy (B)

show abstract

“…Available tools for computing L p -stability and L p -detectability gains of delay dynamics, such as the software HINFN [16], cannot be utilized as they are when a nontrivial B is encountered. Nevertheless, [8, Section 4] delineates how to compute the respective gains in the quotient space R n ξ \ B so that the existing tools can be utilized.…”

Section: B Mass With Nontrivial Sets Bmentioning

confidence: 99%

“…Following [8,Section 4], we introduce the substitution (i.e., change of coordinates) z = (T K ) −1 ξ, where T K is given above for gain K = 2, and prune the last component of z. We now apply the software HINFN [16] to the reduced system in order to compute γ n and γ d for p = 2. For K = 2 we obtain γ n = 3.1588 and γ d = 62.0433, while for K = 4 we obtain γ n = 4.9444 and γ d = 66.5614.…”

Section: Experimental Validationmentioning

confidence: 99%

Multi-agent control in degraded communication environments

Tolić

Palunko

Ivanović

et al. 2015

2015 European Control Conference (ECC)

View full text Add to dashboard Cite

The goal of this paper is to compute transmission rates and delays that provably stabilize Multi-Agent Systems (MASs) in the presence of disturbances and noise. In other words, given the existing information delay among the agents and the underlying communication topology, we determine rates at which information between the agents need to be exchanged such that the MAS of interest is Lp-stable with bias, where this bias accounts for distorted/noisy data. In an effort to consider MASs characterized by sets of equilibrium points, the notions of Lp-stability (with bias) and Lp-detectability with respect to a set are utilized. Using Lyapunov-Razumikhin type of arguments, we are able to consider delays that are greater than the transmission intervals. The present methodology is applicable to general (not merely to single-and double-integrator) heterogeneous linear agents, directed topologies and output feedback. The computed transmission rates are experimentally verified employing a group of off-the-shelf quadcopters.

show abstract

Characterization and Computation of $\mathcal{H}_{\infty}$ Norms for Time-Delay Systems

Cited by 26 publications

References 11 publications

Stabilizing transmission intervals and delays for nonlinear Networked Control Systems: The large delay case

Stabilizing transmission intervals and delays for nonlinear Networked Control Systems: The large delay case

Tuning an H-Infinity Controller with a Given Order and a Structure for Interconnected Systems with Delays

Multi-agent control in degraded communication environments

Contact Info

Product

Resources

About