Robust parametric stability and stabilisation of arbitrary switched linear systems

What is it about?

In this study, robust exponential stability and exponential stabilisation of parametric uncertain switched linear systems are investigated under arbitrary switching. First, sufficient conditions are proposed to ensure the existence of a common quadratic Lyapunov function for arbitrary switched linear systems with uncertain parameters belong to known intervals. Then, an estimation of stability intervals for uncertain parameters is provided via a theorem. To enlarge the estimated stability intervals, an offline optimisation algorithm is also proposed. Finally, the derived results for robust exponential stability are used to stabilise the uncertain switched linear systems which are not stable under arbitrary switching signals. For this purpose, a method is proposed to design a single state feedback gain in the way that the closed-loop switched linear system is robustly exponentially stable under arbitrarily fast switching signals.

Featured Image

Why is it important?

Stability of switched linear systems under arbitrary switching signals is an important requirement, when the switching mechanism is unknown, or too complicated to be useful in the stability analysis. when uncertain systems with parametric uncertainties are investigated, theorems for robust stability of systems with unstructured uncertainties will impose unnecessary conservations. As we should ignore the information about the known structure of uncertainties and include uncertainties, which will never arise in the given system.