Convolution profiles for right inversion of multivariable non-minimum phase discrete-time systems

Marro, G.; Prattichizzo, Domenico; Zattoni, Elena

doi:10.1016/s0005-1098(02)00088-2

Cited by 56 publications

(30 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These problems were described by the authors in [14,15], where geometric-type conditions for perfect or almost perfect tracking or rejection with stability were derived.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

A Nested Computational Approach to the Discrete-Time Finite-Horizon LQ Control Problem

Marro¹,

Prattichizzo²,

Zattoni³

2003

SIAM J. Control Optim.

Self Cite

View full text Add to dashboard Cite

Abstract.A new algorithmic setting is proposed for the discrete-time finite-horizon linear quadratic (LQ) optimal control problem with constrained or unconstrained final state, no matter whether the problem is cheap, singular, or regular. The proposed solution, based on matrix pseudoinversion, is completed and made practically implementable by a nesting procedure for welding optimal subarcs that enables arbitrary enlargement of the control time interval. [17,18,4,22], and Soethoudt, Trentelman and Ran in [21,16]. Extension to cheap and singular problems is obtained by using matrix pencils or linear matrix inequalities.The above contributions mainly refer to continuous-or discrete-time infinitehorizon LQR problems. Conversely, this work focuses on the finite-horizon case for discrete-time systems. It applies to cheap, singular, or regular problems. Considering a sharp constraint on the final state, this paper extends the results given in [16], where the infinite-horizon case with asymptotic endpoint constraints is investigated. However, in the present paper, the requirement that the cost functions are positive semidefinite is still present, while in [16] it is not.From the algorithmic viewpoint, the present work differs from those of the abovementioned papers and is inspired by the system structure algorithm introduced by Silverman in his well-known contribution [20]; see also [19,8]. In the present work, the solution is achieved by the straightforward technique of pseudoinverting a particular system matrix as in [20], but the time interval considered can be arbitrarily

show abstract

“…These problems were described by the authors in [14,15], where geometric-type conditions for perfect or almost perfect tracking or rejection with stability were derived.…”

Section: Discussionmentioning

confidence: 99%

“…Similarly, the optimal extended output sequence e o N , as expressed in (14), can be derived from (26). Remark 1.…”

Section: Statement Of the Problemmentioning

confidence: 99%

A Nested Computational Approach to the Discrete-Time Finite-Horizon LQ Control Problem

Marro¹,

Prattichizzo²,

Zattoni³

2003

SIAM J. Control Optim.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The issue of internal stability of the resulting cascade system was addressed in [14], which considers both left inversion and the dual problem of right inversion. The issue of internal stability and the effect of nonminimum-phase zeros on input reconstruction were addressed within the context of right inversion along with the related notions of noncausal inversion, preview, preaction, and steering along zeros [4,7,8,12,16,20,25]. A unified approach to noncausal right and left inversion is given in [13].…”

Section: Introductionmentioning

confidence: 99%

l-Delay Input and Initial-State Reconstruction for Discrete-Time Linear Systems

Kirtikar

Palanthandalam-Madapusi

Zattoni

et al. 2010

Circuits Syst Signal Process

Self Cite

View full text Add to dashboard Cite

Prior results on input reconstruction for multi-input, multi-output discretetime linear systems are extended by defining l-delay input and initial-state observability. This property provides the foundation for reconstructing both unknown inputs and unknown initial conditions, and thus is a stronger notion than l-delay left invertibility, which allows input reconstruction only when the initial state is known. These properties are linked by the main result (Theorem 4), which states that a MIMO discrete-time linear system with at least as many outputs as inputs is l-delay input and initial-state observable if and only if it is l-delay left invertible and has no invariant zeros. In addition, we prove that the minimal delay for input and state reconstruction is identical to the minimal delay for left invertibility. When transmission zeros are present, we numerically demonstrate l-delay input and state reconstruction to show how the input-reconstruction error depends on the locations of the zeros. Specifically, minimum-phase zeros give rise to decaying input reconstruction error, nonminimumphase zeros give rise to growing reconstruction error, and zeros on the unit circle give rise to persistent reconstruction error.

show abstract

“…The issue of internal stability of the resulting cascade system was subsequently addressed in [5], which considers both left inversion and the dual problem of right inversion. From then on, the issue of internal stability and the effect of nonminimum-phase zeros were tackled within the context of right inversion along with the related notions of noncausal inversion, preview, preaction, and steering along zeros [6]- [12]. A unified solution of noncausal right and left inversion is given in [13].…”

Section: Introductionmentioning

confidence: 99%

l-delay input reconstruction for discrete-time linear systems

Kirtikar

Palanthandalam-Madapusi

Zattoni

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

Self Cite

View full text Add to dashboard Cite

As an extension of existing results on input reconstruction, we define l-delay state and input reconstruction, and we characterize this property through necessary and sufficient conditions. This property is shown to be a stronger notion of left invertibility, in which the initial state is assumed to be known. We demonstrate l-delay state and input reconstruction on several numerical examples, which show how the input reconstruction error depends on the locations of the zeros. Specifically, minimum-phase zeros give rise to decaying input reconstruction error, nonminimum-phase zeros give rise to growing reconstruction error, and zeros on the unit circle give rise to persistent reconstruction error.

show abstract

Convolution profiles for right inversion of multivariable non-minimum phase discrete-time systems

Cited by 56 publications

References 20 publications

A Nested Computational Approach to the Discrete-Time Finite-Horizon LQ Control Problem

A Nested Computational Approach to the Discrete-Time Finite-Horizon LQ Control Problem

l-Delay Input and Initial-State Reconstruction for Discrete-Time Linear Systems

l-delay input reconstruction for discrete-time linear systems

Contact Info

Product

Resources

About