Pole Placement Theorem for Discrete Time-Varying Linear Systems

Babiarz, Artur; Czornik, Adam; Makarov, E. K.; Niezabitowski, Michał; Popova, S. N.

doi:10.1137/15m1033666

Cited by 33 publications

(34 citation statements)

References 34 publications

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“…Then systems (2) and ( 43) are dynamically equivalent. Remark 5: Lemma 4 was proved in [30,Lemma 4.5] for positive semiaxis of integers but the proof remains the same for the whole axes of integers.…”

Section: Dynamic Equivalencementioning

confidence: 94%

“…Denote by Θ(t, τ ) the transition matrix of the free system (43). There is the following criterion of dynamic equivalence [30,Lemma 4.5]. Lemma 4: Suppose that A(t) t∈Z and A(t) t∈Z are Lyapunov sequences.…”

Section: Dynamic Equivalencementioning

confidence: 99%

“…. , λ n (A) ∈ R n ≤ of the free system (2) is well-defined (see [13], [30] for the definition of this concept).…”

Section: Local Assignability Of the Lyapunov Spectrummentioning

confidence: 99%

“…A series of papers [30]- [33] discussed investigations of the problem of Lyapunov exponents placement for discrete-time systems. In these works, sufficient conditions are obtained for the solvability of the problem of assigning the Lyapunov spectrum of discrete non-stationary systems in various formulations.…”

Section: Introductionmentioning

confidence: 99%

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Lyapunov Spectrum Local Assignability of Linear Discrete Time-Varying Systems by Static Output Feedback

et al. 2021

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We consider a linear discrete time-varying input-output system. Our goal is to study the problem of local assignability of the Lyapunov spectrum by static output feedback control. To this end we introduce the notion of uniform consistency for discrete-time linear systems which is the extension of the notion of uniform complete controllability to input-output systems. The property of uniform consistency is investigated, some necessary and sufficient conditions for this property are obtained. The notion of uniform local attainability is introduced for the closed-loop system. We prove that uniform consistency implies uniform local attainability of the closed-loop system. The property of local Lyapunov reducibility is introduced for the closed-loop system. We prove that uniform local attainability implies local Lyapunov reducibility. We prove that, for a locally Lyapunov reducible system, the Lyapunov spectrum is locally assignable, if the free system is diagonalizable or regular (in the Lyapunov sence) or has the stable Lyapunov spectrum.INDEX TERMS linear discrete time-varying input-output systems, local assignability, Lyapunov spectrum, pole assignment problem, static output feedback, uniform consistency.

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Section: Dynamic Equivalencementioning

confidence: 94%

Section: Dynamic Equivalencementioning

confidence: 99%

“…. , λ n (A) ∈ R n ≤ of the free system (2) is well-defined (see [13], [30] for the definition of this concept).…”

Section: Local Assignability Of the Lyapunov Spectrummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lyapunov Spectrum Local Assignability of Linear Discrete Time-Varying Systems by Static Output Feedback

et al. 2021

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“…Note that uniform complete controllability is also a sufficient condition for arbitrary assignability of Lyapunov spectrum of time-varying control systems, see [14,5,4]. Recall that the Lyapunov spectrum of a time-varying system consists of all possible average growth rates of solutions of this system and it is known that the Lyapunov spectrum is a subset of the dichotomy spectrum.…”

Section: Introductionmentioning

confidence: 99%

Assignability of dichotomy spectrum for discrete time-varying linear control systems

Cuong,

Doan

2019

Preprint

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Relative controllability of nonlinear switched fractional systems

Luo,

Liu,

Zhao

et al. 2023

Asian Journal of Control

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This article investigates relative controllability of nonlinear switched fractional systems (SFSs). With the aid of Mittag‐Leffler functions and invariant subspace theory, two sufficient and necessary conditions for corresponding linear SFSs are first established. Then, piecewise continuous control functions and a novel nonlinear operator are constructed to overcome the difficulties arising from switching rules, nonlinearity, and fractional derivatives. Under different constraints on nonlinear functions, two controllability conditions depending on system parameters for nonlinear SFSs are proposed by applying Schauder's and Banach's fixed point theorems, respectively. The obtained criteria may well show the influence of coefficient matrices, fractional derivatives, and switching rules on relative controllability. In addition, our proposed method is also applicable for integer‐order switched systems. Finally, two simulated examples are worked out to verify the theoretical results.

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Pole Placement Theorem for Discrete Time-Varying Linear Systems

Cited by 33 publications

References 34 publications

Lyapunov Spectrum Local Assignability of Linear Discrete Time-Varying Systems by Static Output Feedback

Lyapunov Spectrum Local Assignability of Linear Discrete Time-Varying Systems by Static Output Feedback

Assignability of dichotomy spectrum for discrete time-varying linear control systems

Relative controllability of nonlinear switched fractional systems

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