Design of linear observers for a class of linear hybrid systems

This paper deals with the design of linear observers for a class of linear hybrid systems. Such systems are composed of continuous-time and digital substates and possess, in general, coupling dynamics between both substates. The discrete extended state is composed of the sampled values of the continuous substate at sampling instants and the digital substate. The estimation of the continuous substate in between sampling instants is made by using the plant parametrization and the sampled prediction error at the preceding sampling instant. The continuous-time state estimates are re-initialized at each new sampling instant by taking values from the corresponding components of the discretized substate of the observer of the auxiliary discrete extended system. The exponential convergence to zero of both prediction and observation errors may be ensured under observability and detectability assumptions in both observation prototypes. Furthermore, prescribed pole-placement of the state estimation error is achieved under observability of the discrete extended plant. Also, prescribed pole-placement of the combined dynamics of the extended plant and observation error can be obtained.