Analysis And Synthesis Of Asynchronously Switched Systems Subject To Persistent Dwell-time

Switched system generally refers to a class of hybrid systems composed of multi-ple subsystems and a switching sequence governing signal,called switching signal.Such unique system structure grants switched system the ability of modeling physical object with multiple mode property and describing control systems with multiple controllers,which offers an effective approach in analysis and control synthesis of complex system-s.The application of switched system theory can be found in various practical fields including aerospace and astronautics,auto industry,smart grid,chemistry engineering and disease propagation control.However,there are deficiencies on current research of switched system theory.Most existing studies on time-dependent switching signal focus on dwell-time signal and average dwell-time signal,and attention is seldom paid to persis-tent dwell-time,even though it is of greater generality and stronger capability of describ-ing fast switching.Additionally,research on asynchronous switching between subsystem modes and controllers demands further exploration.Based on former research,this thesis paper systematically investigates control synthesis problem of a class of linear switched systems subject to asynchronous persistent dwell-time,and applies theoretical results to switched system modeling and anti-windup controller design of hypersonic aircraft.The contributions of this thesis paper are as follows:(1)The stability problem of switched system subject to persistent dwell-time with asynchronous switching between system mode and controller is studied.The asynchronous switching primarily refers to the mismatches between system modes and controllers,and generally implies that the switching of controllers fall behind those of system modes in practice.The asynchronous switching can result in an increasing Lyapunov function,and consequently invalid system stability criteria.By adopting the Lyapunov increasing rate,this thesis establishes sufficient conditions of globally uniformly asymptotical stability of switched system subject to asynchronous switching signal,and provides theoretical basis for future controller design as well as filter design problem.(2)The quasi-time-dependent control problem of switched system subject to asyn-chronous persistent dwell-time is studied.Since Multi-Lyapunov-Function based meth-ods generally give sufficient conditions,conservatism is inevitable during controller de-sign,thus introducing negative influence to controller design.This thesis proposes a class of quasi-time-dependent Lyapunov function,and designs quasi-time-dependent s-tate feedback controller and quasi-time-dependent H_?controller for continuous-time and discrete-time switched system,respectively.The conservatism of controller is reduced effectively.(3)The mixed H_?and passive filtering problem of of switched system subject to asynchronous persistent dwell-time is studied.By combining H_?noise attenuation per-formance index and passivity,a mixed H_?and passive performance index is obtained.The mixed H_?and passive filter is designed such that the resulting filtering error system is globally uniformly asymptotically stable with some mixed H_?and passive performance index.The proposed performance index can cover H_?noise attenuation ability and pas-sivity,hence a unified filter design framework is established,which can save some design efforts.(4)The filtering problem of a class of linear parameter varying(LPV)systems with redundant quantizers.Although the amount of data transmission can be reduced,the adop-tion of quantizers can introduce quantization error which may affect system performance.To reduce amount of data transmission without affecting system performance,this thesis constructs a switched system model for LPV system based on selected quantization den-sity.For the sake of conservatism reduction,this thesis proposes a class of quantization-error and system parameter dependent Lyapunov function,upon which a mixed filter is designed.The simulation results indicates that by using switched system theory,the re-quirement of data transmission bandwidth is reduced without seriously affecting system performance.(5)The switched anti-windup control problem of hypersonic aircraft is studied.Due to the wild velocity of hypersonic aircraft and the vast flight airspace,the dynamic model of hypersonic aircraft can present strong nonlinearity and coupling effect,which sug-gests that traditional dynamic model based approach can be unsatisfactory.This thesis presents a flight envelop partitioning based switched system modeling method for hy-personic aircraft,upon which a switched anti-windup controller is designed.Simulation results verify the effectiveness and advantage of proposed switched system model and designed anti-windup controller.