Adaptive state-dependent impulsive observer design for nonlinear deterministic and stochastic dynamics with time-delays. (March 2020) - Kalamian, Nasrin; Khaloozadeh, Hamid; Ayati, S. Moosa
Abstract: The present research has introduced a novel adaptive state-dependent impulsive observer (ASDIO) used to control diverse nonlinear systems with time-varying delay. This designed ASDIO is in conformity with the approach of extended pseudo-linearization for the purpose of parametrizing a nonlinear system with time-delay to a pseudo-linear time-delay structure having state-dependent coefficients. This technique makes the ASDIO applicable to nonlinear systems with distributed, multiple, and time-varying delays. The time-varying and delay-independent Lyapunov functional approach, coupled with the comparison method for impulsive systems, was used to confirm the stability of ASDIO. This new theorem affirmed the state and parameter estimation error to approach zero asymptotically through distinct and less-conservative adequate conditions with respect to practical linear matrix inequalities. Furthermore, the maximum impulse time was specified via the presented stability theorem. The ASDIO has also been offered for a special set of stochastic nonlinear systems with time-delay. An investigation of the asymptotic stability for the intended ASDIO was performed via a new theorem employing the comparison principle for stochastic impulsive systems. Accordingly, this observer was simulated on an epidemic system with time-delay nonlinear features to affirm its performance. Highlights: The ASDIO is applicable in a vast group of nonlinear systems with different time-delay types considering the extended pseudo-linearization approach. The asymptotic convergence of the estimation error for both state and parameter to zero is guaranteed under explicit and less-conservative adequate conditions that are presented concerning feasible LMIs attributed to the comparison system theory. The stability theorem determines an upper bound of time intervals between consecutive impulses, unlike existing methods where the minimum and maximum impulse intervals are regarded as known parameters. The stability theorem contains the special case under Lipschitz condition and the general case of the sector bounded condition. Thus, less-conservative sufficient condition and LMIs with larger feasibility are generated. The ASDIO can evaluate unknown parameters and states for a vast group of stochastic nonlinear time-delay systems under less-conservative adequate conditions stated regarding available LMIs.