On the induced norms of discrete-time and hybrid time-varying systems

Iglesias, Pablo A.; Peters, Marc A.

doi:10.1002/(sici)1099-1239(199709)7:9<811::aid-rnc231>3.0.co;2-f

Cited by 10 publications

(6 citation statements)

References 21 publications

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“…The latter evolves forward in time and so provides an explicit recursive expression for computing the solution to the KYP inequalities (2.6)-(2.7). Similar, but less explicit, results from operator theoretic points of view exist [22,27]. The proof of Lemma 2.5 is based on the following standard lemma.…”

Section: Analysis Of Linear Time-varying Systemsmentioning

confidence: 79%

Optimal Disturbance Attenuation for Discrete‐Time Switched and Markovian Jump Linear Systems

Lee¹,

Dullerud²

2006

SIAM J. Control Optim.

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An exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete-time domain via the union of an increasing family of linear matrix inequality conditions. Associated with each Markovian jump linear system is a switched linear system, so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for Markovian jump linear systems as well. The results lead to semidefinite programming-based controller synthesis techniques, from which optimal finite-path-dependent linear dynamic output feedback controllers arise naturally. In particular, under the notion of path-by-path optimal disturbance attenuation, finite-path-dependent controllers can outperform the usual modedependent ones.

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Section: Analysis Of Linear Time-varying Systemsmentioning

confidence: 79%

Optimal Disturbance Attenuation for Discrete‐Time Switched and Markovian Jump Linear Systems

Lee¹,

Dullerud²

2006

SIAM J. Control Optim.

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“…We typically use the H 2 and H ∞ norms, where the former evaluates the energy of the impulse response while the latter considers the worst energy of the output for the disturbances with unit energy. A number of studies have been conducted for providing analytical solutions for the H 2 optimal control [7][8][9][10] and the H ∞ optimal control [9][10][11][12][13][14][15] of sampled-data systems. However, they cannot be used for dealing with another typical norm called the L ∞ norm, which is associated with bounded persistent disturbances that are often observed in a number of practical control applications.…”

Section: Introductionmentioning

confidence: 99%

L₁ optimal controller synthesis for sampled‐data systems via piecewise linear kernel approximation

Hagiwara

2021

Intl J Robust & Nonlinear

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This article provides a new framework for the so-called L 1 optimal control problem of sampled-data systems, that is, the synthesis problem of a discrete-time optimal controller minimizing the continuous-time L ∞ -induced norm of the closed-loop system for a given continuous-time plant. The main idea is to develop the approximation method called the piecewise linear kernel approximation (PLKA) method, by which the kernel function of the input operator together with the hold function of the output operator in the lifted representation of sampled-data systems are approximated by piecewise linear functions. By defining adequate preadjoint operators, the PLKA method is shown to have the associated convergence rate of 1/N 2 for the deterioration of the attainable L ∞ -induced norm performance when the optimal controller synthesis is conducted approximately under the approximation parameter N.Compared with another existing procedure for controller synthesis through different approximation treatment called the piecewise linear input approximation method, we further show that the proposed PLKA method has a quantitatively improved bound on the performance deterioration. Finally, numerical examples are studied to verify the effectiveness of the proposed PLKA method.

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“…One important aspect of switched systems is their norm computations studied in works such as [5], [6], [7], [8], and [9] for the l 2 induced gain and [10] and [11] for the l ∞ and l 1 induced norm.…”

Section: Introductionmentioning

confidence: 99%

On the characterization of extreme switching sequences

Naghnaeian

Voulgaris

2013

52nd IEEE Conference on Decision and Control

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In this paper, we consider the problem of finding a switching sequence to minimize or maximize the norm of certain classes of linear switched systems in the sense of H 2 , and induced l ∞ or l 1 norm. The motivation is to study certain types of model matching problems including filtering. In particular we show that, for FIR switching system models and induced l ∞ norms, the minimizing switching sequence can be chosen to be periodic.

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On the induced norms of discrete-time and hybrid time-varying systems

Cited by 10 publications

References 21 publications

Optimal Disturbance Attenuation for Discrete‐Time Switched and Markovian Jump Linear Systems

Optimal Disturbance Attenuation for Discrete‐Time Switched and Markovian Jump Linear Systems

L₁ optimal controller synthesis for sampled‐data systems via piecewise linear kernel approximation

On the characterization of extreme switching sequences

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On the induced norms of discrete-time and hybrid time-varying systems

Cited by 10 publications

References 21 publications

Optimal Disturbance Attenuation for Discrete‐Time Switched and Markovian Jump Linear Systems

Optimal Disturbance Attenuation for Discrete‐Time Switched and Markovian Jump Linear Systems

L1 optimal controller synthesis for sampled‐data systems via piecewise linear kernel approximation

On the characterization of extreme switching sequences

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Product

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L₁ optimal controller synthesis for sampled‐data systems via piecewise linear kernel approximation