Algebraic observer for a class of switched systems with zeno phenomenon

Algebraic State Estimation for a Class of Switched Linear Systems

“…This method is based on algebraic tools (differential algebra, module theory and operational calculus) and results in finite time estimates given by explicit algebraic formula that can be implemented in a straightforward manner using standard tools from computational mathematics. Those results have been extended to the problems of closed-loop parametric estimation for continuous-time linear systems in [22] [24], fault diagnosis in [25], nonlinear systems with unknown inputs in [26] or nonlinear feedback control in [27], switched systems estimation with Zeno phenomenon in [28]. This approach was also applied in [29] for the estimation of the index corresponding to the current active subsystem, and the state variable of this subsystem.…”

Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs

“…When this algebraic method is used for numerical differentiation problem, thanks to the proposed integral formulae, it also refers to the differentiation by integration method well known for the Lanczos generalized derivative (see [13] p. 324). The obtained algebraic differentiators have been used to design algebraic nonasymptotic observers for linear and non-linear systems (see, e.g., [14,15,17,18,19]). In the linear case [14,15,16], the proposed differentiators were obtained via the differential equations which define the linear systems.…”

“…The state variables have been accurately estimated without any time-delay. In the non-linear case [17,18,19], the used differentiators were obtained via the equations of truncated Taylor or Jacobi orthogonal series expansions of the output (see [7,8,9] for more details). Hence, these differentiators can be considered as model-free differentiators.…”