Guaranteed Cost Control Of Uncertain Continuous-Time Singular Semi-Markov Jump Systems With Indefinite Quadratic Cost

This paper includes two parts.In the first part.the guaranteed cost control of continuous-time uncertain singular semi-Markov jump systems with indefinite quadratic cost is discussed based on the Lyapunov theory and linear matrix inequality approach.And in the quadratic,the syimmetric weighting matrix is indefinite and may contain the negative eigenvalues.In the second part,the state feedback and static output feedback are respectively designed which guarantee the closed-loop systems t.o be regular,impulse-free,and ro-bust stochastically stable and the cost value is restrict.ed between the lower and upper bounds.The full text is divided into five chapters:Chapter 1 introduces singular systems.Markov jump systems,uncertain semi-Markov jump systems,guaranteed cost control and related theoretical resea.rch status,from which the background of this study and the profound significance of theoretical research are given.Chapter 2 is the preliminary know-ledge.It mainly introduces relatecd lem-mas which is needed t.o prove the theorem in the paper.In Chapter 3,the state feedback guaranteed cost cont.rol for continuous-time unc.ertain singular semi-Markov jump systems with the indefinite quadrat-ic cost is investigated.Firstly,based on Lyapunov stability theory,under the condition of guaranteeing the existence of uncertain guaranteed cost state feedback controllers,the conditions of regular,impulse-free,robust stochastic stability and the bounded value of quadratic cost of closed-loop systems is developed.Secondly,by-using singular value decomposition and linear matrix inequality(LVMI)method to deal with the above sufficient conditions,an LMI sufficient condition is obtained,designing the state feedback controller to guar-ant.ee the close-loop systems is robust stochastically admissible ancd the cost value is restricted between the lower and upper bounds.By solving the LMI,the indefinite guaranteed cost stat,e feedback controller can be obtained.Last-ly a numerical example is given to illustrate the effectiveness of the proposed method.At the same time:when the transition probability is constant,the conclusion is cdeduced.This part was published on The 30th Chinese Control and Decision Conference(2018 CCDC).Clhapter 4 is Imainly about the static out.put feedback guaranteed cost control of uncertain continuous-time singular semi-Markov jump systems with indefinite quadratic cost.Firstly,the conditions of regular,impulse-free,ro-bust stochastic stability and the bounded value of quadratic cost of closed-loop systems is developed.Next,by using matrix decoupling technique and a new linear matrix inequality-method,an LMI sufficient condition is obtained,designing the static output,feedback controller to guarantee the close-loop sys-tems is robust stochastically admissible and the cost value is restricted between the lower and upper bounds.By solving the LMI,the indefinite guaranteed cost static output feedback controller can be obtained.Lastly a numerical example is given to illustrate the effectiveness of the proposed method.At the same time,when the transition probability is constant,the conclusion is de-duced.This part was published on The 37th Chinese Control Conference(2018 CCC).Finally,Chapter 5 concludes this thesis.