Observer-based tracking control design for periodic piecewise time-varying systems

Abstract

In this study, the problem of robust tracking problem for continuous-time periodic piecewise time-varying delay systems with disturbances and uncertainties has been examined by using observer-based H∞ tracking control protocol. Precisely, the state space representation of the system is formulated to reconstruct the unmeasurable states via the available informations of input/output dynamics. Based on the suitable Lyapunov-Krasovskii functional with periodic piecewise time-varying Lyapunov matrix, a set of sufficient conditions in the form of linear matrix inequalities is derived which affirms the robust asymptotic tracking performance and satisfactory disturbance attenuation for the addressed model. Particularly, the matrix polynomial approach is utilized which makes the analysis to be more flexible and amenable to convex optimization tool. Accordingly, the period time-varying controller and observer gains are computed through the feasible solution of derived matrix inequalities. Conclusively, the simulation results are presented to confirm the efficiency and applicability of the theoretical outcomes.