Comprehensive Study On Control Of Uncertain Saturated Systems With Multiple Time Delays

In practical feedback control systems,actuator saturation and time delays often coexist,and ignoring their presence may lead to a decrease in closed-loop system performance or even instability.This paper aims to study the control problem of uncertain saturated multiple time-delay systems.To address the shortcomings and limitations of existing methods,a corresponding distributed-delay-dependent polytopic approach and sector conditions dependent on time delay are proposed by utilizing multiple time delays information and characteristics of the system,which are used to deal with the saturation nonlinearity in the multiple time-delays system and reduce the conservatism of the method.Meanwhile,combining with the corresponding actuator saturation model and time-delay-related stability analysis methods,the control strategies of these two types of systems are studied,and the estimation and optimization design problems of the attraction domain are discussed.This study provides theoretical support for the application of practical control systems,improves and enriches existing results,and all control design conditions are represented by linear matrix inequalities(LMIs),making it easy to solve using existing standard software.The main research work of this paper includes the following aspects:First,the control problem of uncertain saturated linear system with multiple time delays is considered.Distributed-delay-dependent polytopic approach is proposed by using some cross-terms related to multiple different time delays,and a new type of Lyapunov-Krasovskii functional is constructed.Based on this,stability and robust stability conditions are proposed in the form of linear matrix inequalities by further introducing Wirtinger integral inequalities and Jensen inequalities.These conditions guarantee that the closed-loop systems are asymptotically stable for admissible initial conditions.Simulation examples demonstrate the feasibility and advantages of the obtained results.Secondly,the control problem of uncertain input-saturated system with multiple time delays under discrete time conditions is considered.A new sector condition dependent on time delay is proposed,and dead-zone nonlinear functions are introduced to transform saturation nonlinearity into dead-zone nonlinearity for solving.Based on this,using the augmented Lyapunov-Krasovskii functional with discrete properties,time-delay-dependent sector conditions,discrete Wirtinger inequalities,and some congruence transformations,we establish the stability conditions and robust stability conditions of the closed-loop system with multiple delays in discrete time and propose the design method of state feedback controller as well as the estimation and optimization design method of attraction domain.Finally,we validate the effectiveness of the proposed results through numerical examples and simulations.