Stabilization of Nonlinear Systems by Switched Lyapunov Function

If a Lyapunov function is known, a dynamic system can be stabilized. However, computing a Lyapunov function is often challenging. This paper takes a new approach; it assumes a basic Lyapunov-like function then seeks to numerically diminish the Lyapunov value. If the control effort would have no effect at any iteration, the Lyapunov-like function is switched in an attempt to regain control. The method is tested on four simulated systems to give some perspective on its usefulness and limitations. A highly coupled 3rd order system demonstrates the approach’s general applicability and finally the coordinated control of 7 motors for a robotic application is considered. Details on the publicly available software packages for application agnostic software and hardware environments are also presented.

Robust Admissibility Analysis of Switched Singular Systems with Linear Fractional Uncertainties

This paper considers the problem of robust admissibility analysis of uncertain discrete-time switched linear singular systems for arbitrary switching laws. The parameter uncertainties are assumed to be of linear fractional form. By using the switched Lyapunov function approach, some new sufficient conditions ensuring such systems to be admissible for arbitrary switching laws are presented in terms of linear matrix inequalities (LMIs). Example is provided to demonstrate the effectiveness of the obtained results