Stability Analysis And Control Synthesis Of Uncertain Impulsive Systems

Impulsive systems are a class of hybrid systems,which have both the properties of continuous-time dynamics and discrete-time impulsive effects.Up to now,impulsive systems theories find a wide variety of applications including ecology,biomedicine,economics,communications,aerospace,control and other fields.Analysis and synthesis of impulsive systems are even more challenging due to their complex dynamics and some physical constraints like model uncertainty,external disturbance,positive characteristics,nonlinear characteristics,and time delay.There are still many problems of analysis and synthesis for impulsive systems to be deal with.On the basis of the existing research results and analysis methods,this dissertation focuses on the issues of stability analysis,performance analysis,robust control and practical applications for several classes of uncertain impulsive dynamic systems.The main topics covered in this dissertation can be summarized as follows:Chapter 2 investigates the problems of robust stability and H_?performance analysis and controller design for a class of Lipschitz nonlinear impulsive systems with periodic impulses,and application to the sampled-data system filter design is also studied.In order to better reflect the reality,model uncertainty,continuous-time and discrete-time disturbance inputs are taken into consideration.Firstly,the stability and H_?performance analysis issue is formulated as the existence problem of solution for a nonlinear matrix differential equation with two-point boundary value.Subsequently,the proposed two-point boundary value problem is formulated as the feasibility problem of a couple of linear matrix inequalities,which can be easily verified.Based on the obtained stability and H_?performance results,the robust H_?control problem is further investigated.A sufficient condition for the existence of an H_?state feedback controller is obtained.Finally,the proposed theoretical results are applied to design the H_?filter for sampled-data systems.This chapter generalizes the existing theoretical results,while also enriching the application of impulsive systems theories in the analysis and synthesis of sampled-data systems.Chapter 3 is concerned with the robust stability analysis,L₁-gain performance anal-ysis and control design for interval uncertain linear impulsive positive systems,and its application to the traffic control system is also investigated.In order to better describe the disturbance attenuation performance,a general L₁-gain performance is defined for impul-sive positive systems,which is a natural extension of the classical L₁-gain performance.First,by employing the idea of impulse interval partitioning,a piecewise time-varying copositive Lyapunov function is proposed to analyze the robust stability of the considered system.The obtained robust asymptotic stability condition depends on both the upper and the lower bounds of impulse intervals and is less conservative than the existing results.By using hypothetical reasoning,it is proved that increasing the discretizing parameter is beneficial to reduce the conservatism of obtained results.We further employ the proposed piecewise time-varying copositive Lyapunov function to analyze the L₁-gain performance for the case where external disturbances are considered.Subsequently,based on the obtained stability and L₁-gain criteria,the positive robust stabilization problem is investi-gated.A sufficient condition is formulated for the existence of state-feedback controllers with which not only the positivity and robust stability of the resulting closed-loop system are guaranteed,but also a prescribed L₁-gain performance is satisfied simultaneously.Furthermore,to make the controller synthesis problem numerically tractable,we pro-pose an iterative algorithm to compute the desired controller parameters.Finally,several numerical examples and a practical traffic control example are presented to show the effectiveness and applicability of the proposed methodology.This part can be regarded as an improvement of the existing results on stability analysis for linear impulsive positive systems,and also fills the gap in the field of L₁-gain performance analysis.It is worthwhile pointing out that the proposed piecewise time-varying copositive Lyapunov function will be applied to deal with some related issues in Chapter 4 and Chapter 5.Chapter 4 considers the robust stability and stabilization of impulsive positive delay systems with polytopic uncertainty.First,by using the piecewise time-varying copositive Lyapunov function proposed in Chapter 3 and Razumikhin technique,we establish the robust exponential stability criterion that depends on both the upper and the lower bounds of impulse intervals,which is also less conservative than the existing results.The obtained stability condition is further adopted to solve the robust positive stabilization problem,and a sufficient condition is formulated for the existence of state-feedback controllers.The desired controller parameters can be computed by a heuristic iterative algorithm.The stability criteria proposed in this chapter relax the conservatism of the existing sufficient stability conditions.Meanwhile it develops the robust stability analysis and control theories of uncertainty impulsive positive delay systems.Chapter 5 is concerned with the stability analysis and L₁-gain characterization for nonlinear impulsive positive systems,and its application to the integrated pest management is also investigated.According to the fact that Takagi-Sugeno?T-S?fuzzy models can approximate any nonlinear system to any accuracy,the concerned nonlinear impulsive positive system is described by the corresponding T-S fuzzy impulsive systems.Therefore,based on the T-S fuzzy impulsive systems,a sufficient condition guaranteeing the positivity of this kind of system is proposed.Subsequently,the exponential stability criterion that relies on both the lower and the upper bounds of impulsive intervals is established by employing the piecewise time-varying copositive Lyapunov function proposed in Chapter3.Subsequently,with the help of hypothetical reasoning analysis method,it is proved that increasing the discretizing parameter is beneficial to reduce the conservatism of obtained results.For the case where external disturbances are considered,the L₁-gain result is derived for the concerned systems by using the proposed piecewise time-varying copositive Lyapunov function.Finally,a numerical example and a practical integrated pest management example are presented to show the effectiveness and applicability of the proposed methodology.The researches of this chapter not only enrich the theoretical results about stability and performance analyses for nonlinear impulsive positive systems,but also provides useful theoretical evidences that can be referred to for synthesis problems of nonlinear impulsive positive systems.