A new shift-invariant representation for periodic linear systems

Flamm, David S.

doi:10.1016/0167-6911(91)90093-t

Cited by 60 publications

(32 citation statements)

References 6 publications

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“…and consider cyclic shift-invariant lifted LTI system (7) with x ∈ R n , u ∈ R m (Bittanti & Colaneri, 2000;Flamm, 1991;Park & Verriest, 1989):…”

Section: Periodic Set Invariancementioning

confidence: 99%

“…An appropriate definition for (maximum) periodic positively (Definition 3) and controlled (Definition 4) invariant sets is proposed here, and a method for their determination based on cyclic shift-invariant lifting (Bittanti & Colaneri, 2000;Flamm, 1991;Park & Verriest, 1989) and invariant set methods for LTI systems (Blanchini, 1999;Dória & Hennet, 1999;Gilbert & Tan, 1991) is presented. Very closely related polyhedral maximum periodic controlled invariant sets were considered in Blanchini and Ukovich (1993).…”

Section: Introductionmentioning

confidence: 99%

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MPC of constrained discrete-time linear periodic systems — A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

Linares

Jones

2011

Automatica

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a b s t r a c tState-feedback model predictive control (MPC) of discrete-time linear periodic systems with timedependent state and input dimensions is considered. The states and inputs are subject to periodically time-dependent, hard, convex, polyhedral constraints. First, periodic controlled and positively invariant sets are characterized, and a method to determine the maximum periodic controlled and positively invariant sets is derived. The proposed periodic controlled invariant sets are then employed in the design of least-restrictive strongly feasible reference-tracking MPC problems. The proposed periodic positively invariant sets are employed in combination with well-known results on optimal unconstrained periodic linear-quadratic regulation (LQR) to yield constrained periodic LQR control laws that are stabilizing and optimal. One motivation for systems with time-dependent dimensions is efficient control law synthesis for discrete-time systems with asynchronous inputs, for which a novel modeling framework resulting in low dimensional models is proposed. The presented methods are applied to a multirate nano-positioning system.

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“…and consider cyclic shift-invariant lifted LTI system (7) with x ∈ R n , u ∈ R m (Bittanti & Colaneri, 2000;Flamm, 1991;Park & Verriest, 1989):…”

Section: Periodic Set Invariancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

MPC of constrained discrete-time linear periodic systems — A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

Linares

Jones

2011

Automatica

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“…Norm of the transfer operator for such system can be computed in similar way as for linear time-invariant systems. More description for the lifting technique for periodic time-varying systems can be found in [30][31][32][33][34]37].…”

Section: Corollarymentioning

confidence: 99%

Generalized feedback stability for periodic linear time-varying, discrete-time systems

Orłowski¹

2012

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The paper proposes a novel method for feedback stability evaluation for linear time-varying, discrete-time control systems. It is assumed that the time-varying system can be described by the general discrete-time, time-varying state space model and by the equivalent linear input-output (transfer) operator. The method extends feedback stability concepts for systems given in a general linear time-varying, discrete-time form, not only in the Lurie form. In the paper selected short-time stability concepts are employed for inference about feedback stability of systems defined on an infinite time-horizon. Theoretical considerations are complemented by numerical examples.

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“…Lifting (Flamm 1991) is a well-known technique to transform a periodic system (1) into a timeinvariant one. Applied to (2), this leads to a block cyclic matrix pencil…”

Section: Introductionmentioning

confidence: 99%

Matlab Tools for Solving Periodic Eigenvalue Problems

Granat

Kågström

Kreßner

2007

IFAC Proceedings Volumes

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Software for computing eigenvalues and invariant subspaces of general matrix products is proposed. The implemented algorithms are based on orthogonal transformations of the original data and thus attain numerical backward stability, which enables good accuracy even for small eigenvalues. The prospective toolbox combines the efficiency and robustness of library-style Fortran subroutines based on state-of-the-art algorithms with the convenience of Matlab interfaces. It will be demonstrated that this toolbox can be used to address a number of tasks in systems and control theory, such as the solution of periodic discrete-time algebraic Riccati equations.

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A new shift-invariant representation for periodic linear systems

Cited by 60 publications

References 6 publications

MPC of constrained discrete-time linear periodic systems — A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

MPC of constrained discrete-time linear periodic systems — A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

Generalized feedback stability for periodic linear time-varying, discrete-time systems

Matlab Tools for Solving Periodic Eigenvalue Problems

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