In order to solve the state estimation problem for linear hybrid systems with periodic jumps and unknown inputs, some hybrid observers are proposed. The proposed observers admit a Luenberger-like structure and the synthesis is given in terms of linear matrix inequalities (LMIs). Therefore, the proposed observer designs are completely constructive and provide some input-to-state stability properties with respect to unknown inputs. It is worth mentioning that the structure of the hybrid observers, as well as the structure of the LMIs, depends on some observability properties of the flow and jump dynamics, respectively. Then, in order to compensate the effect of the unknown inputs, a hybrid sliding-mode observer is added to the Luenberger-like observer structure, providing exponential convergence to zero of the state estimation error despite certain class of unknown inputs. The existence of the hybrid observers and the unknown input hybrid observer is guaranteed if and only if the hybrid system is observable and strongly observable, respectively. Some numerical examples illustrate the feasibility of the proposed estimation approach.
|Number of pages||23|
|Journal||International Journal of Robust and Nonlinear Control|
|State||Published - 1 Oct 2020|
Bibliographical noteFunding Information:
Air Force Office of Scientific Research, FA9550‐15‐1‐0155; FA9550‐18‐1‐0246; Consejo Nacional de Ciencia y Tecnología, 270504; Instituto Politécnico Nacional, SIP‐IPN 20195310 Funding information
information Air Force Office of Scientific Research, FA9550-15-1-0155; FA9550-18-1-0246; Consejo Nacional de Ciencia y Tecnolog?a, 270504; Instituto Polit?cnico Nacional, SIP-IPN 20195310H. R?os gratefully acknowledges the financial support from C?tedras CONACYT CVU 270504 and project 922; J. D?vila gratefully acknowledges the financial support from SIP-IPN under grant 20195310. Research also supported in part by AFOSR grants FA9550-15-1-0155 and FA9550-18-1-0246, and NSF grant ECCS-1508757.
H. Ríos gratefully acknowledges the financial support from Cátedras CONACYT CVU 270504 and project 922; J. Dávila gratefully acknowledges the financial support from SIP‐IPN under grant 20195310. Research also supported in part by AFOSR grants FA9550‐15‐1‐0155 and FA9550‐18‐1‐0246, and NSF grant ECCS‐1508757.
© 2020 John Wiley & Sons, Ltd.
- hybrid systems
- linear systems
- observer design