On the distinguishability and observer design for single-input single-output continuous-time switched affine systems under bounded disturbances with application to chaos-based modulation

Abstract Switched Affine Systems ( SAS ׳ s ) is a class of Hybrid Systems composed of a collection of Affine Systems ( AS ׳ s ) and a switching signal that determines, at each time instant, the evolving affine subsystem. This paper is concerned with the observability and observer design for single-input single-output ( SISO ) SAS ׳ s under unknown perturbation, for the case that no information about the switching signal is available. It is firstly demonstrated that in the presence of disturbances every pair of AS ׳ s is always indistinguishable from the continuous output, meaning that it is not possible to infer the evolving AS by using only the information provided by the output of the SAS . Nevertheless, by taking advantage of the knowledge on the disturbance bound, new distinguishability conditions are derived, making possible to distinguish the evolving AS . By using these new distinguishability conditions, an observer scheme for SISO SAS ׳ s , subject to unknown switching signal and unknown perturbations, is presented. Such an observer scheme determines in finite-time the evolving AS . Furthermore, it estimates both the state of the system and the disturbance. Finally, the proposed observer scheme is effectively applied for a non-autonomous chaotic modulation application, which is an attractive method for spread-spectrum secure communication in which the message is fed as a disturbance to a chaotic SAS and the output is then transmitted through an open channel to a receiver, which is an observer algorithm that recovers the message (the disturbance) from the output signal.