Dissipative Control Problem For Singular Time-delay Systems

In recent years, the research on the time delay systems attracts considerableattention in the control theory literature all along. In practical problems, thetime-delay usually leads to a decline in the performance of the whole system, andeven instability. The main consideration in this article is the design of dissipative andcontroller under the delay-dependent in singular time-delay systems. The study ofdissipativity contains system regular, impulse-free (causal and effect), stability andthe relationship between stored energy function and supply rate, so the research ofdissipativity is more complex. This paper mainly studies the dissipative of linearsystem and discrete system. This paper is organized as follows:(1)The paper introduces the research background and development status ofgeneralized systems, then we introduces the development of the dissipative theory ingeneralized systems and the importance of the systems, and lastly we introduces thedevelopment status of time-delay systems and the significance of the research.(2) We mainly study the problem of delay-dependent α-dissipativity control forsingular systems with time-delay. The first reference gives the definition of linearstrictly (Q, S, R)-α-dissipative. The sufficient conditions are established in terms oflinear matrix inequalities (LMIs), which guarantees a singular system to beadmissible and strictly (Q, S, R)-α-dissipative.Then, we design state feedbackcontroller for singular systems with time-delays and time-delay state feedbackcontroller, the closed-loop system is strictly dissipative. Finally, numerical examplesare given to illustrate the effectiveness of the presented results.(3) We mainly study the problem of delay-dependent α-dissipativity control fordiscrete singular systems with time-delay. The sufficient conditions are established interms of linear matrix inequalities by introducing new Lyapunov-functions, whichguarantees a singular system to be admissible and strictly (Q, S, R)-α-dissipative.Then, we design state feedback controller for singular systems with time-delays andtime-delay state feedback controller, the closed-loop system is strictly dissipative.Finally, numerical examples are given to illustrate the effectiveness of the presentedresults.(4) We summarizes this dissertation and shows the further study in this field.