Stability theory for linear time-invariant plants with periodic digital controllers

Francis, Bruce A.; Georgiou, Tryphon T.

doi:10.1109/9.1310

Cited by 392 publications

(137 citation statements)

References 19 publications

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“…Lemma 5.1: The equilibrium of the linear HDS determined by the system of equations (18) is uniformly asymptotically stable if and only if the matrix (21) is Schur stable, where (22) The conclusion of Lemma 5.1 is well known (refer, e.g., to [10] and [11]). …”

Section: Application To Nonlinear Sampled-data Systemsmentioning

confidence: 99%

Stability theory for hybrid dynamical systems

Michel

Hou

1998

IEEE Trans. Automat. Contr.

697

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Abstract-Hybrid systems which are capable of exhibiting simultaneously several kinds of dynamic behavior in different parts of a system (e.g., continuous-time dynamics, discrete-time dynamics, jump phenomena, switching and logic commands, and the like) are of great current interest. In the present paper we first formulate a model for hybrid dynamical systems which covers a very large class of systems and which is suitable for the qualitative analysis of such systems. Next, we introduce the notion of an invariant set (e.g., equilibrium) for hybrid dynamical systems and we define several types of (Lyapunov-like) stability concepts for an invariant set. We then establish sufficient conditions for uniform stability, uniform asymptotic stability, exponential stability, and instability of an invariant set of hybrid dynamical systems. Under some mild additional assumptions, we also establish necessary conditions for some of the above stability types (converse theorems). In addition to the above, we also establish sufficient conditions for the uniform boundedness of the motions of hybrid dynamical systems (Lagrange stability). To demonstrate the applicability of the developed theory, we present specific examples of hybrid dynamical systems and we conduct a stability analysis of some of these examples (a class of sampleddata feedback control systems with a nonlinear (continuous-time) plant and a linear (discrete-time) controller, and a class of systems with impulse effects).

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Section: Application To Nonlinear Sampled-data Systemsmentioning

confidence: 99%

Stability theory for hybrid dynamical systems

Michel

Hou

1998

IEEE Trans. Automat. Contr.

697

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“…Digital control is also an environment where multirate systems are used either to overcome practical difficulties or to achieve unattainable results by single rate control [1,2,3,4]. In fact Dual-rate systems in systems and control have long ago been of interest to engineers [5]: low-latency measurements, limited-speed actuators in control loops, fast sensing in order to better filter measurement noise, network load [6,7], computational resources [8], zeroassignment [9], etc.…”

Section: Motivationmentioning

confidence: 99%

A new algorithm for dual-rate systems frequency response computation in discrete control systems

Salt

Sala

2014

Applied Mathematical Modelling

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ElsevierSalt Llobregat, JJ.; Sala Piqueras, A. (2014) AbstractThis paper addresses an easy computation of the multiple components of the response to a sinusoidal input of a dual-rate linear time-invariant discrete system from the Bode diagram of LTI systems arising from a lifted representation. Based on those results, a generalized Bode diagram is suggested. Some new conclusions derived from this conceptual interpretation are introduced. This diagram provides a better insight in the frequency-response issues in multivariable control than the standard Singular Value Decomposition of the lifted model. As an application, the output ripple suppression in a multirate control scheme is presented.

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“…The number of contributions on linear time-varying discrete-time periodic systems has been increasing in recent times; see, e.g., [15,19,22,45,47,49] and the references therein. This increasing interest in periodic systems has also been motivated by the large variety of processes that can be modelled through linear discrete-time periodic systems (e.g., multirate sampled-data systems, chemical processes, periodically time-varying filters and networks, and seasonal phenomena [2,3,7,16,28,33,51]). …”

Section: Introductionmentioning

confidence: 99%

Projected Generalized Discrete-Time Periodic Lyapunov Equations and Balanced Realization of Periodic Descriptor Systems

Chu¹,

Fan²,

Lin³

2007

SIAM J. Matrix Anal. & Appl.

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From the necessary and sufficient conditions for complete reachability and observability of periodic time-varying descriptor systems, the symmetric positive semi-definite reachability/observability Gramians are defined. These Gramians can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method for solving these projected Lyapunov equations, and an illustrative numerical example is given. As an application of our results, the balanced realization of periodic descriptor systems is discussed.

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Stability theory for linear time-invariant plants with periodic digital controllers

Cited by 392 publications

References 19 publications

Stability theory for hybrid dynamical systems

Stability theory for hybrid dynamical systems

A new algorithm for dual-rate systems frequency response computation in discrete control systems

Projected Generalized Discrete-Time Periodic Lyapunov Equations and Balanced Realization of Periodic Descriptor Systems

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