Stability for a Multi-Rate Sampled-Data System

Stanford, David P.

doi:10.1137/0317029

Cited by 54 publications

(14 citation statements)

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“…That is, any two states in the controllable subspace of the original (continuous-time) system can be driven to each other via appropriate synchronous switching and (piecewise constant) digital control. One contribution of this result lies in the fact that there has already been done a lot of work for discretetime switched linear systems [10][11][12]. Due to the above connection, the tools for discrete-time systems can be utilized to investigate continuous-time systems and the existing results can be converted into parallel results for the continuous-time counterpart.…”

Section: Introductionmentioning

confidence: 94%

Sampling and control of switched linear systems

Sun

2004

Journal of the Franklin Institute

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Section: Introductionmentioning

confidence: 94%

Sampling and control of switched linear systems

Sun

2004

Journal of the Franklin Institute

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“…In the theory of the joint/lower spectral radius, the Berger-Wang theorem [2,5,8,18] plays a significant role. This theorem makes it possible to express the joint and lower spectral radii by means of equalities (14) and (15), respectively. In this connection, the following problems arise.…”

Section: Other Minimax Characteristics Of Matrix Productsmentioning

confidence: 99%

Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems

Kozyakin¹

2019

Discrete &Amp; Continuous Dynamical Systems - B

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To estimate the growth rate of matrix products An · · · A1 with factors from some set of matrices A, such numeric quantities as the joint spectral radius ρ(A) and the lower spectral radiusρ(A) are traditionally used. The first of these quantities characterizes the maximum growth rate of the norms of the corresponding products, while the second one characterizes the minimal growth rate. In the theory of discrete-time linear switching systems, the inequality ρ(A) < 1 serves as a criterion for the stability of a system, and the inequalityρ(A) < 1 as a criterion for stabilizability.For matrix products AnBn · · · A1B1 with factors Ai ∈ A and Bi ∈ B, where A and B are some sets of matrices, we introduce the quantities µ(A, B) and η(A, B), called the lower and upper minimax joint spectral radius of the pair {A, B}, respectively, which characterize the maximum growth rate of the matrix products AnBn · · · A1B1 over all sets of matrices Ai ∈ A and the minimal growth rate over all sets of matrices Bi ∈ B. In this sense, the minimax joint spectral radii can be considered as generalizations of both the joint and lower spectral radii. As an application of the minimax joint spectral radii, it is shown how these quantities can be used to analyze the stabilizability of discrete-time linear switching control systems in the presence of uncontrolled external disturbances of the plant.

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“…As an example of a problem in which such a question arises let us consider one of the varieties of the stabilizability problem for discrete-time switching linear systems [1][2][3][4][5]. Consider a system whose dynamics is described by the equations x(n) = A n u(n), A n ∈ A,…”

Section: Introductionmentioning

confidence: 99%

On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices

Kozyakin

2018

Discrete Dynamics in Nature and Society

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We consider the problem of convergence to zero of matrix products ⋅ ⋅ ⋅ 1 1 with factors from two sets of matrices, ∈ A and ∈ B, due to a suitable choice of matrices { }. It is assumed that for any sequence of matrices { } there is a sequence of matrices { } such that the corresponding matrix products ⋅ ⋅ ⋅ 1 1 converge to zero. We show that, in this case, the convergence of the matrix products under consideration is uniformly exponential; that is, ‖ ⋅ ⋅ ⋅ 1 1 ‖ ≤ , where the constants > 0 and ∈ (0, 1) do not depend on the sequence { } and the corresponding sequence { }. Other problems of this kind are discussed and open questions are formulated.

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Stability for a Multi-Rate Sampled-Data System

Cited by 54 publications

References 1 publication

Sampling and control of switched linear systems

Sampling and control of switched linear systems

Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems

On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices

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