Stability Analysis And Control Synthesis Of Incommensurate Impulsive Switched Systems

Impulsive switched systems belong to one of the hybrid systems,which have widely ap-plication in quite a few areas,such as robot control systems,flight control systems and network communication,etc.Impulsive switched systems can be used to model and describe a family of continuous dynamics with instantaneous state jumps and the discrete switching events among them.It has been proven that the overall performance of a system is no longer the simple compo-sition of its subsystems.When introduced as a control method,impulsive and switching behavior also enrich the design of system control.With the engineering and industrial systems becom-ing large scale,networked,the networked control problems of impulsive switched systems are turning into international frontiers and challenging hotspots,such as the varying sampled-data control problem.Up till now,most of the existing literature focus on the case where switches and impulses are synchronous.The research on impulsive switched systems where the impulses are not required to synchronise the switching is still in its infancy and has many restricts.When introduced unknown disturbance and nonlinear impulsive increment,a number of issues induced by the coupling of impulses,switching and sampling need to be addressed urgently.This disser-tation aims to solve the aforementioned problems and the work is summarized as follows.For uncertain impulsive switched systems with time varying uncertainties and nonlinear im-pulsive increments,robust H_?control is studied.The impulses are not required to synchronize the switching.Instead,the impulse sequences follow an average impulsive interval assump-tion,in which the restriction on common lower(or upper)bound of two consecutive impulses is dropped.By using the multiple Lyapunov function and average dwell time(ADT)method,even with high impulse frequency,the robust H_?control performance can still be guaranteed under the proposed sufficient conditions.Finally,switched feedback controllers are designed to guarantee that the system is robust H_?stabilizable with certain disturbance attenuation level.The input-to-state stability(ISS)of time-delay incommensurate impulsive switched systems is studied.The impulses are not required to synchronise the switching.Moreover,we allow that time-delay effects can exist in both the continuous dynamics and impulses.Sufficient conditions for ISS are constructed by using the method of multiple Lyapunov–Krasovskii functionals.It is shown that,when all the subsystems are ISS,the time-delay impulsive switched system as a whole can still retain the ISS property if the average number of impulses and switching during any time period is not too big.It means the requirement on common lower bound of two consecutive impulses is dropped because we only require the impulses follow an average impulsive interval condition.On the other hand,even if all the subsystems are not ISS,we can construct impulses occurring not too sparsely on average to stabilize the system in the ISS sense.Based on the above results on the traditional control of incommensurate impulsive switched systems,we further consider the varying sampled-data control of incommensurate impulsive switched systems with asynchronous switching.The impulses are not required to synchronise the switching.The switch inside the sampling interval can lead to mismatch between the model and its corresponding controller.This behavior is formulated and analyzed.Aiming for this,a functional consisting of multiple impulse-dependent Lyapunov functions and looped function-als is constructed,which does not increase at impulsive times.By using ADT method,some sufficient conditions for exponential stability are proposed in terms of linear matrix inequalities.Furthermore,sampled-data controllers are presented to stabilise the impulsive switched systems.At last,the obtained result is applied to F-18 aircraft.