Special Topics On Stability Analysis Of Time Delay Systems

The delay or aftereffect phenomenon is prevalent in the real physical world. Timedelay systems (shortly, TDS, also called hereditary systems, systems with memory,time-lag or dead-time) belong to the class of functional differential equations (FDEs)which are infinite-dimensional, as opposed to ordinary differential equations (ODEs).The complexity of systems' properties and dynamic performances is a real challengeto the analysis and synthesis of such systems. For both theoretical and practicalimpacts, time delay systems have been an enduring theme for the automation andcontrol academia for several decades. A great number of monographs andlucubrations have been devoted to this field of active, extensive and comprehensiveresearch.The stability analysis of time delay system is the subject of this thesis, and thecontinous time system with delay is the research object. With respect to thesystematical framework of theories and the abundance of practical approaches of theformer research, the author is mainly focused on the original problems or the newpersepective and resolvent of common problems. In time domain, based on theLyapunov stability theory (mainly by using Lyapunov-Krasovskii Theorem), theanalytical approches are utilized through the whole thesis with the help of LinearMatrix inequality. Attention has also been paid in frequency domain, with theconsideration of the convenience in the computional aspect. The main contents andnovelty of this thesis are outlined as follows,1. For the fundamental TDS of retarded type, the asymptotical stability criterion isgiven in the integral form. From the numerical comparison of the existingtypically important results, the theoretical analysis of the conservatism is given,the equivalence of a serial of criterions is proven, and the concision andprecision of our criterion is shown. The integral form criterion is furtherimproved in the neutral type TDS with distributed delay. And associated withparameter-dependent technology, the sufficient conditions for robust stability ofthe relavent uncertain systems are given.2. From the problem of the stability of simplified distributed TDS with theαconstraint, a general class of distributed TDS is introduced. For this class ofTDS, a novel quasi-polytope model transformation is offered based on theconvex sum property. By using this transformation, the existing computionalcomplexity is removed, and a memoryless state-feedback H_∞controller is thengiven. 3. The novel D stability problem of TDS is investigated. The state transformationof the system is made both in time domain and frequency domain with respectto the system's properties. Results are obtained in the unified framework ofLypunov stability theory, and the conservatism introduced by matrix measure inprevious work is hence avoided.4. For the interval TDS, a Lyapunov-Krasovskii type stability criterion is given intime domain, and a quasi-polynomials based test is given in frequency domain.A comparative study is made to see the advantage and disadvantage of both.