Robust stability bounds on time-varying perturbations for state-space models of linear discrete-time systems

Kolla, Sri R.; Yedavalli, Rama K.; Farison, James B.

doi:10.1080/00207178908953354

Cited by 130 publications

(30 citation statements)

References 8 publications

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“…where the constants in 0 s have the same sign as the corresponding parameters. Note that [8] has no counterpart of 20 and 52p is inferior to ap. Also, the largest sphere with its center at the origin which is included in 0 s is given by (6.9) and is smaller than a?.…”

Section: ~~~' ( A~p a )~~' ( P~)mentioning

confidence: 99%

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Robust stability of discrete-time systems under parametric perturbations

Karan

Sezer

Ocali

1994

IEEE Trans. Automat. Contr.

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of time varying linear systems," IEEE Trans. Automat. Contr., vol. 33, pp. 150-155, 1988. B. E. Ydstie, "Stability of discrete model reference control revisited," Syst. Contr. Lett., vol. 13, pp. 429438, 1989. -, "Stability of the direct self-tuning regulator," in Foundations of Adaptive Control, P. V. Kokotovic, Ed., 1991, pp. 201-238 [61-[81).The main objective of this paper is to link the stability robustness problem of discrete-time systems to that of continuous-time systems. We show, using two different approaches, that stability robustness of a discrete-time system can be reformulated as that of an auxiliary continuous-time system. One of these approaches makes use of Lyapunov theory and yields a sufficient condition. The second approach, which is based on the properties of Kronecker products, provides a necessary and sufficient condition at the expense of an increase in the dimensionality. This is a pleasing development, since it allows for a direct application of the known results on stability robustness bounds for continuous-time systems to discrete-time systems. The results are applied to stability analysis of interconnected systems, where the interconnections are treated as perturbations on a collection of stable subsystems. This demonstrates how a knowledge of the structure of perturbations can be exploited to obtain simple robustness bounds. PROBLEM STATEMENT Robust Stability of Discrete-Time Systems Under Parametric PerturbationsConsider a discrete-time system under additive multiparameter perturbations, which is described as Mehmet Karan, M. Erol Sezer, and Ogan Ocali Absfract-Stability robustness analysis of a system under parametric perturbations is concerned with characterizing a region in the parameter space in which the system remains stable. In this paper, two methods are presented to estimate the stability robustness region of a linear, time-invariant, discrete-time system under multiparameter additive perturbations. An inherent difficulty, which originates from the nonlinear appearance of the perturbation parameters in the inequalities defining the robustness region, is resolved by transforming the problem to stability of a higher order continuous-time system. This allows for application of the available results on stability robustness of continuous-time systems to discrete-time systems. The results are also applied to stability analysis of discrete-time interconnected systems, where the interconnections are treated as perturbations on decoupled stable subsystems.

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Section: ~~~' ( A~p a )~~' ( P~)mentioning

confidence: 99%

“…This restriction was relaxed in [9] and applied to river pollution control. Linear uncertain systems with state delay were treated in [8] …”

Section: Design Of Robust Controllers For Time-delay Systemsmentioning

confidence: 99%

Robust stability of discrete-time systems under parametric perturbations

Karan

Sezer

Ocali

1994

IEEE Trans. Automat. Contr.

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“…Kolla and Farison (1990) use the idea of state transformation to reduce the conservatism of the previous results (Kolla et al 1989). The idea may also be used here.…”

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confidence: 98%

New robust stability bounds of linear discrete-time systems with time-varying uncertainties

Fong

1993

International Journal of Control

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“…Sufficient conditions for robust stability, based on the Lyapunov approach, had been proposed in [11][12][13][14]. Given a positive-definite function V (X), system (9) asymptotically converges 8 to the equilibrium with convergence rate 0 < µ < 1 if the difference V (X(k + 1)) − µV (X(k)) is negative for any k ≥ 0.…”

Section: Robust Stability Of Time-varying Linear Systemsmentioning

confidence: 99%

“…The design problem on non-uniform discrete-time domains can be successfully approached by exploiting interesting results on robust stability (see [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]) for perturbed systems of type…”

Section: Robust Stability Of Time-varying Linear Systemsmentioning

confidence: 99%

Controller Synthesis on Non-uniform and Uncertain Discrete–Time Domains

Balluchi¹,

Murrieri²,

Sangiovanni‐Vincentelli

2005

Hybrid Systems: Computation and Control

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Abstract. The problem of synthesizing feedback controllers that perform sensing and actuation actions on non-uniform and uncertain discrete time domains is considered. This class of problems is relevant to many application domains. For instance, in engine control a heterogenous and, to some extent, uncertain event-driven time domain is due to the behavior of the 4-stroke internal combustion engine, with which the controller has to synchronize to operate properly. Similar problems arise also in standard discrete-time control systems when considering the behavior of the system with controller implementation and communication effects. The design problem is formalized in a hybrid system framework; synthesis and verification methods, based on robust stability and robust performance results, are presented. The effectiveness of the proposed methods is demonstrated in an engine control application.

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Robust stability bounds on time-varying perturbations for state-space models of linear discrete-time systems

Cited by 130 publications

References 8 publications

Robust stability of discrete-time systems under parametric perturbations

Robust stability of discrete-time systems under parametric perturbations

New robust stability bounds of linear discrete-time systems with time-varying uncertainties

Controller Synthesis on Non-uniform and Uncertain Discrete–Time Domains

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