Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory

This paper presents the robust stabilization problem of linear and non-linear fractional-order systems with non-linear uncertain parameters. The uncertainty in the model appears in the form of the combination of 'additive perturbation' and 'multiplicative perturbation'. Sufficient conditions for the robust asymptotical stabilization of linear fractional-order systems are presented in terms of linear matrix inequalities (LMIs) with the fractional-order 0 < α < 1. Sufficient conditions for the robust asymptotical stabilization of non-linear fractional-order systems are then derived using a generalization of the Gronwall-Bellman approach. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.

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“…Lemma 3.2 (Khargonakar et al, 1990) Let X and Y be real vectors of the same dimension. Then, for any scalar δ > 0, the following inequality holds…”

Section: Stability Results For Fractional-order Dynamic Systemsmentioning

confidence: 99%

On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

Ndoye

Darouach

Voos

et al. 2015

IMA J Math Control Info

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“…For this, it follows from (3.6)-(3.8) that Integrating both sides of (3.14), we have 2 clt, t £ ( 4 , a (3.15) [7] Robust Woo stabilisation 477…”

Section: Is the Maximum Eigenvalue Of P^\(l + D K ) T P Ik (I + D K )mentioning

confidence: 99%

“…The main focus has been on H^ problems for linear systems [2,10], nonlinear systems [9], and systems without delay as well as with delays [2,5,9,10] and so on. In recent years, interest has been extended to the robust Hoc stability problem of impulsive dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

Robust H_∞ stabilisation with definite attenuance of an uncertain impulsive switche system

Xu¹,

Liu

Teo

2005

ANZIAM J.

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In this paper, we study the problem of robust //«, stabilisation with definite attenuance for a class of impulsive switched systems with time-varying uncertainty. A norm-bounded uncertainty is assumed to appear in all the matrices of the state model. An LMI-based method for robust/Zoo stabilisation with definite attenuance via a state feedback control law is developed. A simulation example is presented to demonstrate the effectiveness of the proposed method.

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“…Research addressing the problems of ∞ H and positive real control systems can be found in (Safonov et al 1987, Doyle et al 1989, Haddad and Bernstein 1991, Sun et al 1994. Control of uncertain linear systems with 2 Lbounded structured uncertainty satisfying ∞ H and passivity criteria have been tackled in (Peterson 1987, Khargonekar et al 1990). More recent development involving the quadratic dissipative control for linear systems problem has been tackled in (Xie et al 1998, Tan et al 2000.…”

Section: Dissipativity Performance Includesmentioning

confidence: 99%

Robust and Resilient State Dependent Control of Discrete-Time Nonlinear Systems with General Performance Criteria

Wang

Yaz

2011

IFAC Proceedings Volumes

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A novel state dependent control approach for discrete-time nonlinear systems with general performance criteria is presented. This controller is robust for unstructured model uncertainties, resilient against bounded feedback control gain perturbations in achieving optimality for general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state dependent linear matrix inequality at each time step, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H ∞ and positive real control to provide a novel robust control design. The effectiveness of the proposed technique is demonstrated by simulation of the control of inverted pendulum.

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Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory

Cited by 1,398 publications

References 25 publications

On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

Robust H_∞ stabilisation with definite attenuance of an uncertain impulsive switche system

Robust and Resilient State Dependent Control of Discrete-Time Nonlinear Systems with General Performance Criteria

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Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory

Cited by 1,398 publications

References 25 publications

On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

Robust H∞ stabilisation with definite attenuance of an uncertain impulsive switche system

Robust and Resilient State Dependent Control of Discrete-Time Nonlinear Systems with General Performance Criteria

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Product

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Robust H_∞ stabilisation with definite attenuance of an uncertain impulsive switche system