Control
Theory for Linear Systems

Trentelman, Harry L.; Stoorvogel, Anton A.; Hautus, Mlj Malo; Dewell, Larry

doi:10.1115/1.1497472

Cited by 38 publications

(36 citation statements)

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“…In particular matrixĀ 22 represents, in the given coordinates, the map induced on V * /R * by A (Th. 7.14Trentelman et al, 2001). Note that under item 2 of Assumption 1, the pair , is stabilizable, as it can be easily verified by the PBH test.…”

mentioning

confidence: 81%

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On input allocation-based regulation for linear over-actuated systems

Galeani¹,

Serrani

Varano³

et al. 2015

Automatica

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mentioning

confidence: 81%

“…By V * ⊂ R n , we denote the weakly unobservable subspace for P , i.e., the set of initial conditions for which there exists an input function such that the ensuing output is identically zero. It is well known (Trentelman, Stoorvogel, & Hautus, 2001) that V * is the largest subspace V ⊂ R n such that…”

Section: Assumptionmentioning

confidence: 99%

On input allocation-based regulation for linear over-actuated systems

Galeani¹,

Serrani

Varano³

et al. 2015

Automatica

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“…The following definition of invariant zeros is a direct generalization of the finitedimensional case in [26,32]. This concept has been introduced by Rosenbrock [23], where it is called input-output-decoupling zeros.…”

Section: Invariant Zerosmentioning

confidence: 99%

Zero dynamics and root locus for a boundary controlled heat equation

Reis

Selig

2015

Math. Control Signals Syst.

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We consider single-input single-output systems whose internal dynamics are described by the heat equation on some domain Ω ⊂ R d with sufficiently smooth boundary ∂Ω. The scalar input is formed by the Neumann boundary values which are forced to be constant in space; the output consists of the integral over the Dirichlet boundary values. We show that the transfer function admits some partial fraction expansion with positive residues. The location of the transmission zeros and invariant zeros is further analyzed. Thereafter we show that the zero dynamics are fully described by a self-adjoint and exponentially stable semigroup. The spectrum of its generator is proven to be the set of invariant zeros. Finally, we show that any positive proportional output feedback results in an exponentially stable system. We further analyze the root loci: as the proportional gain tends to infinity, the eigenvalues of the generator of the closed-loop system converge to the invariant zeros.

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“…Some basic definitions for strong observability, strong detectability, invariant zeroes, relative degree, and dwell time are introduced in this section (see, e.g., [46][47][48] and [2]). Consider an LTI system…”

Section: 12mentioning

confidence: 99%

Non‐minimum phase switched systems: HOSM‐based fault detection and fault identification via Volterra integral equation

Ríos

Efimov

Dávila

et al. 2013

Adaptive Control & Signal

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In this paper, the problem of continuous and discrete state estimation for a class of linear switched systems with additive faults is studied. The class of systems under study can contain non-minimum phase zeroes in some of their 'operating modes'. The conditions for exact reconstruction of the discrete state are given using structural properties of the switched system. The state space is decomposed into the strongly observable part, the non-strongly observable part, and the unobservable part, to analyze the effect of the unknown inputs. State observers based on high-order sliding mode to exactly estimate the strongly observable part and Luenberger-like observers to estimate the remaining parts are proposed. For the case when the exact estimation of the state cannot be achieved, the ultimate bounds on the estimation errors are provided. The proposed strategy includes a high-order sliding-mode-based fault detection and a fault identification scheme via the solution of a Volterra integral equation. The feasibility of the proposed method is illustrated by simulations.

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Control Theory for Linear Systems

Cited by 38 publications

References 0 publications

On input allocation-based regulation for linear over-actuated systems

On input allocation-based regulation for linear over-actuated systems

Zero dynamics and root locus for a boundary controlled heat equation

Non‐minimum phase switched systems: HOSM‐based fault detection and fault identification via Volterra integral equation

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