M18 – ISTANBUL 18/04/2016 – 22/04/2016

Stability and Stabilisation of Time-varying systems [Lyapunov stability without Lyapunov functions]

Elena Panteley
Laboratoire des Signaux et Systèmes (L2S)
CNRS-CentraleSupélec-U PSUD, France
      Antonio Loria
     Laboratoire des Signaux et Systèmes (L2S)
     CNRS-CentraleSupélec-U PSUD, France

Abstract  of the course

This course focusses on the nonlinear control problems related to physical systems such as robots, marine vehicles, motors, etc. Realistic scenarios impose uncertainties in the parameters and the impossibility of measuring the whole system's state. Solving such problems through systematic Lyapunov-based design may rapidly become intractable only because of our inability to construct strict Lyapunov functions.

We study a number of analysis methods (alternative to Lyapunov’s) which allow to establish strong properties of stability and robustness in scenarios of tracking control problems, dynamic output-feedback, observer-based separation principle for physical systems. These methods generalise well-known results for autonomous systems, such as Lasalle’s invariance principle, to the case of time-varying systems.


• Integrability conditions (Refinements of  Barbalat);
• Differential methods reminiscent of Lasalle’s invariance principle (Matrosov);
• Adaptive control and closed-loo identification;
• Dynamic output-feedback  and invariance principle;
• Linear time-varying systems and consensus;


• Robot tracking control;
• Sensorless control of electrical motors;    
• Formation control of autonomous vehicles;
• Nonholonomic systems;
• Synchronisation.