Displaying similar documents to “Control Lyapunov functions and stabilization by means of continuous time-varying feedback”

Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs

Mehmet Emir Koksal (2016)

Open Mathematics

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Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct...

On finite time stability with guaranteed cost control of uncertain linear systems

Atif Qayyum, Alfredo Pironti (2018)

Kybernetika

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This paper deals with the design of a robust state feedback control law for a class of uncertain linear time varying systems. Uncertainties are assumed to be time varying, in one-block norm bounded form. The proposed state feedback control law guarantees finite time stability and satisfies a given bound for an integral quadratic cost function. The contribution of this paper is to provide a sufficient condition in terms of differential linear matrix inequalities for the existence and...

Control Lyapunov functions and stabilization by means of continuous time-varying feedback

Iasson Karafyllis, John Tsinias (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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For a general time-varying system, we prove that existence of an “Output Robust Control Lyapunov Function” implies existence of continuous time-varying feedback stabilizer, which guarantees output asymptotic stability with respect to the resulting closed-loop system. The main results of the present work constitute generalizations of a well known result due to Coron and Rosier [J. Math. Syst. Estim. Control 4 (1994) 67–84] concerning stabilization of autonomous systems by means of time-varying...

Adaptive stabilization of coupled PDE–ODE systems with multiple uncertainties

Jian Li, Yungang Liu (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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The adaptive stabilization is investigated for a class of coupled PDE-ODE systems with multiple uncertainties. The presence of the multiple uncertainties and the interaction between the sub-systems makes the systems to be considered more general and representative, and moreover it may result in the ineffectiveness of the conventional methods on this topic. Motivated by the existing literature, an infinite-dimensional backsteppping transformation with new kernel functions is first introduced...

Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems

ludovic faubourg, jean-baptiste pomet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the so-called “Jurdjevic-Quinn conditions”. For these systems a positive definite function is known that can only be made non increasing by feedback. We describe how a control Lyapunov function can be obtained a deformation of this “weak” Lyapunov function. Some examples are presented, and the linear quadratic situation is treated as an illustration. ...

Robust aperiodic-disturbance rejection in an uncertain modified repetitive-control system

Lan Zhou, Jinhua She, Chaoyi Li, Changzhong Pan (2016)

International Journal of Applied Mathematics and Computer Science

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This paper concerns the problem of designing an EID-based robust output-feedback modified repetitive-control system (ROFMRCS) that provides satisfactory aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. An equivalent-input-disturbance (EID) estimator is added to the ROFMRCS that estimates the influences of all types of disturbances and compensates them. A continuous-discrete two-dimensional model is built to describe the EID-based...

Quadratic stabilization of distributed parameter systems with norm-bounded time-varying uncertainty.

Wanyi Chen, Fengsheng Tu (1997)

Collectanea Mathematica

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This note focuses on the study of robust H-sub-infinity control design for a kind of distributed parameter systems in which time-varying norm-bounded uncertainty enters the state and input operators. Through a fixed Lyapunov function, we present a state feedback control which stabilizes the plant and guarantees an H-sub-infinity norm bound on disturbance attenuation for all admissible uncertainties. In the process, we generalize some known results for finite dimensional linear systems....