A robust Sliding Mode Controller for a class of SISO bilinear delayed systems

In this paper we propose a Sliding Mode Controller for a class of scalar bilinear systems with delay in both the input and the state. Such a class is considered since it has shown to be suitable for modelling and control of a class of turbulent flow systems. The stability and robustness analysis for the reaching phase in the controlled system are Lyapunov-based. However, since the sliding dynamics is infinite dimensional and described by an integral equation, we show that the stability and robustness analysis is simplified by using Volterra operator theory.

[1]  Feingesicht Maxime,et al.  A bilinear input-output model with state-dependent delay for separated flow control , 2016 .

[2]  Andrey Polyakov,et al.  SISO model‐based control of separated flows: Sliding mode and optimal control approaches , 2017 .

[3]  Olof J. Staffans,et al.  Volterra Integral and Functional Equations: Index , 1990 .

[4]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[5]  Sing Kiong Nguang,et al.  Comments on "Robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation" , 2001, Autom..

[6]  Leonid M. Fridman,et al.  Stability notions and Lyapunov functions for sliding mode control systems , 2014, J. Frankl. Inst..

[7]  Laurentiu Hetel,et al.  Binary Control Design for a Class of Bilinear Systems: Application to a Multilevel Power Converter , 2016, IEEE Transactions on Control Systems Technology.

[8]  G. Ladas,et al.  Oscillation Theory of Delay Differential Equations: With Applications , 1992 .

[9]  Emilia Fridman,et al.  Introduction to Time-Delay Systems , 2014 .

[10]  L. Berezansky,et al.  Nonoscillation Theory of Functional Differential Equations with Applications , 2012 .

[11]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[12]  Maxime Feingesicht.  Nonlinear active control of turbulent separated flows : Theory and experiments , 2017 .

[13]  L. Debnath.  Nonlinear Partial Differential Equations for Scientists and Engineers , 1997 .

[14]  Miroslav Krstic,et al.  Flow Control by Feedback: Stabilization and Mixing , 2010 .

[15]  Vadim I. Utkin,et al.  Sliding mode control in electromechanical systems , 1999 .

[16]  B. R. Noack,et al.  Closed-Loop Turbulence Control: Progress and Challenges , 2015 .

[17]  Andrei Polyakov,et al.  Minimization of disturbances effects in time delay predictor-based sliding mode control systems , 2012, J. Frankl. Inst..