Event‐based output feedback control of periodic systems: A piecewise impulsive method

Abstract

In this article, an event‐triggered control with periodic time‐varying parameters is designed to stabilize a class of periodic systems with exogenous disturbances in a network environment. The continuous‐time periodic system is approximated by some linear subsystems with finite‐number constant matrices based on a piecewise method. It can thus reduce the complexity of theoretical analysis. To tackle the reduction of unnecessary data transmission between the sensor (or controller) and the controller (or actuator), new event‐triggering mechanisms are designed via output feedback. Special parameters are designed to eliminate Zeno behavior, and the minimum triggering interval is obtained according to the designed condition. Then, an event‐triggered periodic piecewise system is modeled as an impulsive periodic piecewise system. The bounded stability, as well as the L∞ performance of the impulsive periodic piecewise system, are analyzed. Furthermore, the gains of the event‐triggered controller are obtained by a method of variable substitution. Finally, the validity of the proposed control is demonstrated by an application example.

Design of proportional integral observer‐based resilient control for periodic piecewise time‐varying systems: The finite‐time case

“…4 Thereupon, the researchers used a piecewise approximation methodology to meet all the issues in the continuous-time periodic time-varying systems, which led to the inception of the periodic piecewise systems (PPSs). [5][6][7][8][9] To be more precise, PPSs are formulated by dissecting the fundamental period of the continuous-time periodic time-varying systems into a certain number of subintervals, wherein the behavior of each subinterval is governed by its accompanying subsystem. Further, it is imperative to emphasize that the subsystems associated with the PPSs can be either time-invariant or time-variant.…”

“…On grounds of this, the Floquet factorization technique is adopted in the analysis of continuous‐time periodic time‐varying systems, however, this technique lacks closed‐form solutions 4 . Thereupon, the researchers used a piecewise approximation methodology to meet all the issues in the continuous‐time periodic time‐varying systems, which led to the inception of the periodic piecewise systems (PPSs) 5–9 . To be more precise, PPSs are formulated by dissecting the fundamental period of the continuous‐time periodic time‐varying systems into a certain number of subintervals, wherein the behavior of each subinterval is governed by its accompanying subsystem.…”

Disturbance Observer-Based Robust Control Design for Uncertain Periodic Piecewise Time-Varying Systems With Disturbances

“…solutions [6], [7], [8]. In order to confront this difficulty, the periodic piecewise systems (PPSs) has been introduced, which aids in simplifying the analysis of the system and making dynamical results more accurate [9], [10]. To be more specific, PPSs are defined by partitioning the specified fundamental period of continuous-time periodic systems into several subintervals, where performance within each subinterval is governed by a related subsystem.…”

Tracking control design for periodic piecewise polynomial systems with multiple disturbances

“…Piecewise methodology, in particular, becomes a more appropriate way by partitioning each period into a set number of segments by a given interval. In this regard, continuous‐time systems are approximated as periodic piecewise systems (PPSs) and it is found to be the most advantageous and effective way 7‐13 . More interestingly in Reference 8, a matrix polynomial technique is taken into consideration to accomplish the stability and stabilization problem of periodic piecewise linear systems (PPLSs).…”

“…In this regard, continuous-time systems are approximated as periodic piecewise systems (PPSs) and it is found to be the most advantageous and effective way. [7][8][9][10][11][12][13] More interestingly in Reference 8, a matrix polynomial technique is taken into consideration to accomplish the stability and stabilization problem of periodic piecewise linear systems (PPLSs). The authors in Reference 9 proposed a resilient fault-tolerant controller for the PPLSs subject to uncertainties, disturbances and actuator fault, which affirms the asymptotic stability of the system.…”