Unknown input observer of switched system with non detectable and non stabilisable mode with application to control of system with constant Unknown input

This work proposes an unknown input observer, a classical observer, and an observer-based controller for switched linear systems with non-detectable and non-stabilizable modes. Sufficient conditions for observer synthesis are formulated as LMIs. The results, extended to observer-based control, rely on a switched Lyapunov function and average dwell time for system convergence. Two examples illustrate the methodology: an academic case for comparison with existing approaches and a buck converter, a benchmark for switched systems.