On controllability of driftless inhomogeneous bilinear systems

Tie, Lin

doi:10.1109/cdc.2014.7039877

Cited by 6 publications

(4 citation statements)

References 27 publications

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“…A consequence is that the discretization "drift" is not particularly useful for improving the controllability properties of a system. This is coherent with the conclusion of [21] that the system (25) is not controllable and neither "nearly-controllable".…”

Section: B "Drifting" With a Single Control Inputsupporting

confidence: 88%

“…4. Comparing Euler and exact discretization of (21). The Euler discretization (22) (in blue) shows a geometric phase.…”

Section: Geometric Phase and Discretization Error For Driftless mentioning

confidence: 99%

“…For this it is enough to consider a single-input discrete-time system in R 2 , like (see [21], Lemma 4).…”

Section: B "Drifting" With a Single Control Inputmentioning

confidence: 99%

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Nonintegrable discrete-time driftless control systems: Geometric phases beyond the area rule

Altafini

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-In a continuous-time nonlinear driftless control system, a geometric phase is a consequence of nonintegrability of the vector fields, and it describes how cyclic trajectories in shape space induce non-periodic motion in phase space, according to an area rule. The aim of this paper is to shown that geometric phases exist also for discrete-time driftless nonlinear control systems, but that unlike their continuous-time counterpart, they need not obey any area rule, i.e., even zeroarea cycles in shape space can lead to nontrivial geometric phases. When the discrete-time system is obtained through Euler discretization of a continuous-time system, it is shown that the zero-area geometric phase corresponds to the gap between the Euler discretization and an exact discretization of the continuous-time system.

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Section: B "Drifting" With a Single Control Inputsupporting

confidence: 88%

“…4. Comparing Euler and exact discretization of (21). The Euler discretization (22) (in blue) shows a geometric phase.…”

Section: Geometric Phase and Discretization Error For Driftless mentioning

confidence: 99%

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Nonintegrable discrete-time driftless control systems: Geometric phases beyond the area rule

Altafini

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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“…The controller design is not applicable to systems such as Example in with the parameter λ =0. In that example, the origin is on the border of the stabilizable region, and no continuous Lyapunov function can be used to prove stability.…”

Section: Discussionmentioning

confidence: 99%

Control design for discrete‐time bilinear systems using the scalarized Schur complement

Vatani

Hovd

Olaru

2017

Intl J Robust & Nonlinear

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Summary In this paper, controller design for discrete‐time bilinear systems is investigated by using sum of squares programming methods and quadratic Lyapunov functions. The class of rational polynomial controllers is considered, and necessary conditions on the degree of controller polynomials for quadratic stability are derived. Next, a scalarized version of the Schur complement is proposed. For controller design, the Lyapunov difference inequality is converted to a sum of squares problem, and an optimization problem is proposed to design a controller, which maximizes the region of quadratic stability of the bilinear system. Input constraints can also be accounted for. Copyright © 2017 John Wiley & Sons, Ltd.

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On controllability, near-controllability, controllable subspaces, and nearly-controllable subspaces of a class of discrete-time multi-input bilinear systems

Tie

2016

Systems & Control Letters

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On controllability of driftless inhomogeneous bilinear systems

Cited by 6 publications

References 27 publications

Nonintegrable discrete-time driftless control systems: Geometric phases beyond the area rule

Nonintegrable discrete-time driftless control systems: Geometric phases beyond the area rule

Control design for discrete‐time bilinear systems using the scalarized Schur complement

On controllability, near-controllability, controllable subspaces, and nearly-controllable subspaces of a class of discrete-time multi-input bilinear systems

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