Asymptotic Stability of Second-Order Linear Time-Varying Systems

Okano, Ryotaro; Kida, Takashi; Nagashio, Tomoyuki

doi:10.2514/1.24283

Cited by 14 publications

(14 citation statements)

References 4 publications

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“…In this section, we present the integral function approach to the exponential stability analysis of LTV systems (1). The integral function is defined, analyzed and used to determine the exponential stability of LTV systems.…”

Section: Resultsmentioning

confidence: 99%

“…Definition 1 Let x(t, t 0 ; z) denote the solution of system (1) with initial state z. The LTV system (1) is called exponentially stable if there exist r ∈ (0, 1) and κ r > 0 such that…”

Section: Problem Formulationmentioning

confidence: 99%

“…Examples of LTV systems are: (1) Space station carrying moving vehicles [1]; (2) Aircraft affected by the nearly periodic nature of the Earth's magnetic field [2];…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability and performance analysis of linear time-varying systems with application to the international space station

She

Zhang

et al. 2014

Proceedings of 2014 IEEE Chinese Guidance, Navigation and Control Conference

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This paper introduces a novel and rapid approach for the stability and performance analysis of linear time-varying (LTV) systems, which has a very wide application to the evaluation of control system of Aerospace vehicles. By introducing the concept of integral function for the LTV systems and showing its prosperities, a sufficient and necessary condition for the exponential stability of LTV systems is derived. Furthermore, by computing the radii of convergence of the integral function, the exponential decay rate of system trajectories of LTV systems can be obtained exactly, which provides a computable way for the analysis of system performance. Finally, the algorithm for computing the integral function is developed and the proposed approach is applied to the stability and performance analysis of the control system of international space station.

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Section: Resultsmentioning

confidence: 99%

“…Definition 1 Let x(t, t 0 ; z) denote the solution of system (1) with initial state z. The LTV system (1) is called exponentially stable if there exist r ∈ (0, 1) and κ r > 0 such that…”

Section: Problem Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Stability and performance analysis of linear time-varying systems with application to the international space station

She

Zhang

et al. 2014

Proceedings of 2014 IEEE Chinese Guidance, Navigation and Control Conference

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“…(17) It can also be shown that V (x,t) is decrescent and therefore x = 0 is uniformly asymptotically stable if all eigenvalues of M(t),D(t) andK(t) are bounded [17].…”

Section: Theoremmentioning

confidence: 98%

Static output feedback controller design based on LMI for linear time-varying collocated mechanical system

Takaku

Nagashio

Kida

2014

11th IEEE International Conference on Control &Amp; Automation (ICCA)

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This paper studies a static output feedback control for linear time-varying collocated mechanical systems. The internal stability and L 2 gain control performance conditions are first derived by utilizing specific system structures. Then we propose a controller design algorithm based on linear matrix inequality to obtain gain-scheduled optimal feedback gains. Simple numerical studies are shown and discussed.

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“…Although unlike linear time-invariant systems, stability of linear time-varying systems does not depend on only whether the characteristic value lies in the left half complex plane [16][17][18], the characteristic value of B remains always on the right hand side, and those of C enter in the right hand side some times; hence the instability of B and C is expected. The next example is chosen as a stable second-order system.…”

Section: Examplementioning

confidence: 99%

Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs

Köksal

2016

Open Mathematics

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Necessary and sufficiently conditions are derived for the decomposition of a second order linear timevarying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation of the system itself.

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Asymptotic Stability of Second-Order Linear Time-Varying Systems

Cited by 14 publications

References 4 publications

Stability and performance analysis of linear time-varying systems with application to the international space station

Stability and performance analysis of linear time-varying systems with application to the international space station

Static output feedback controller design based on LMI for linear time-varying collocated mechanical system

Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs

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