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Stability Analysis of a Family of Continuous State Feedback Synthesis: Theory and Experiments

Raúl Santiesteban-Cos, Araceli Gárate-García*, and Oscar Montaño-Godinez
International Journal of Control, Automation, and Systems, vol. 15, no. 3, pp.1011-1019, 2017

Abstract : "A family of continuous state feedback synthesis based on sliding mode control is analyzed using a Lyapunov approach, such that the compensation of growing perturbations together with state variables is shown. Robustness properties of a family of controllers, varying from the well known twisting sliding mode control law to the PD controller, are studied. A non-smooth Lyapunov function is proposed such that global finite-time stability of the origin is demonstrated and tuning rules for the control gains are obtained. Moreover, since the Lyapunov function is strict, an upper bound for the convergence time of the closed loop system can be estimated, in spite of the growing perturbations with respect to the state. To illustrate the performance and robustness properties of the feedback synthesis, experimental results are presented, using a one-link pendulum as a test bed."

Keyword : Convergence-time estimation, Lyapunov function, second-order sliding modes, stability analysis.

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