Robust state feedback control of LTV systems: Nonlinear is better than linear

Bianchini, Franco; Megretski, Alexandre

doi:10.23919/ecc.1997.7082456

Cited by 10 publications

(12 citation statements)

References 11 publications

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“…Actually, it was later pointed out that the Petersen counterexample is indeed linearly stabilizable (but not via a quadratic Lyapunov function [Sta95b,Sta95a]). The final claim has been proved in [BM99b].…”

Section: Limits Of Quadratic Functions and Linear Controllersmentioning

confidence: 76%

“…We will give a very simple example soon. The third claim has been proved in [BM99b]. The fourth claim is much more difficult and the reader is referred to the famous Petersen counterexample [Pet85].…”

Section: Limits Of Quadratic Functions and Linear Controllersmentioning

confidence: 96%

“…It is worth saying that there are examples of stabilizable systems which cannot be stabilized via linear (even dynamic) compensators. The interested reader is again referred to [BM99b].…”

Section: Example 717 (Stabilizability and Quadratic Stabilizability mentioning

confidence: 99%

“…This can be done by means of a very simple counterexample (which is taken and suitably adapted from [BM99b]). Consider the LPV systemẋ…”

Section: Theorem 754 System (753) Can Be Stabilized By a Gain Schementioning

confidence: 99%

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Set-Theoretic Methods in Control

Blanchini

Miani

2015

Systems &Amp; Control: Foundations &Amp; Applications

209

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Section: Limits Of Quadratic Functions and Linear Controllersmentioning

confidence: 76%

Section: Limits Of Quadratic Functions and Linear Controllersmentioning

confidence: 96%

“…It is worth saying that there are examples of stabilizable systems which cannot be stabilized via linear (even dynamic) compensators. The interested reader is again referred to [BM99b].…”

Section: Example 717 (Stabilizability and Quadratic Stabilizability mentioning

confidence: 99%

“…This can be done by means of a very simple counterexample (which is taken and suitably adapted from [BM99b]). Consider the LPV systemẋ…”

Section: Theorem 754 System (753) Can Be Stabilized By a Gain Schementioning

confidence: 99%

See 2 more Smart Citations

Set-Theoretic Methods in Control

Blanchini

Miani

2015

Systems &Amp; Control: Foundations &Amp; Applications

209

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“…Furthermore we show that in the gain scheduling case, nonlinear compensator cannot outperform linear ones. This is in contrast with the robust stabilization case in which nonlinear controller can outperform linear ones [9] (see also [21] for further implications). Thus limiting the attention to linear compensator is not a restriction for gain scheduling state-feedback stabilization.…”

Section: Introductionmentioning

confidence: 90%

Stabilization of LPV Systems: State Feedback, State Estimation, and Duality

Blanchini

Miani

2003

SIAM J. Control Optim.

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In this paper, the problem of the stabilization of Linear Parameter Varying systems by means of Gain Scheduling Control, is considered This technique consists on designing a controller which is able to update its parameters on-line according to the variations of the plant parameters. We first consider the state feedback case and we show a design procedure based on the construction of a Lyapunov function for discrete-time LPV systems in which the parameter variations are affine and occur in the state matrix only. This procedure produces a nonlinear static controller. We show that, differently from the robust stabilization case, we can always derive a linear controller, that is nonlinear controllers cannot outperform linear ones for the gain scheduling problem. Then we show that this procedure has a dual version which leads to the construction of a linear gain scheduling observer. The two procedures may be combined to derive an observer-based gain scheduling compensator.

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How conservative is the circle criterion?

Megretski

1999

Open Problems in Mathematical Systems and Control Theory

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Robust state feedback control of LTV systems: Nonlinear is better than linear

Cited by 10 publications

References 11 publications

Set-Theoretic Methods in Control

Set-Theoretic Methods in Control

Stabilization of LPV Systems: State Feedback, State Estimation, and Duality

How conservative is the circle criterion?

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