Robust H_∞Control For Time-delay Systems And Application Research On Networked Control

Time delays are widely encountered in various industrial, physicaland engineering systems, they are often sources of degradation and ins-tability of the performance in control systems. Therefore, the research onstability analysis of time-delay systems has been a hot issue in the con-trol field, and has been of great interest to a large number of researchers.On the other hand, the aim of robust H_∞control problem of time-delaysystems is to design the suitable controllers such that the systems areasymptotically stable under the condition with a given H_∞performanceindexγ, which is an important research subject both in theory and inpractice.In this paper, based on the current research status of robust H_∞control theory and the existing conclusions, the delay-dependent robuststability of systems with time-varying delay and H_∞controller designproblem are investigated firstly. Networked control systems with rand-omly varying delay and missing measurements are then considered byapplying the theory of time-delay systems. The detailed research con-tents and conclusions are as follows:1) The delay-dependent robust stability of a class of systems withtime-varying delay is discussed by the Lyapunov’s second method. First,for time-delay d (t)in two cases: One case is continuous but non-diff-erentiable time-varying delay; the other is differentiable time-varyingdelay. A new Lyapunov-Krasovskii functional is constructed by employ-ing a delay decomposition technique. And combining with reciprocallyconvex approach, new delay-dependent bounded real conditions are ob-tained, which guarantee that the system is asymptotically stable. Numer-ical example simulations are finally given to demonstrate the effective-ness of the obtained results.2) The delay-dependent robust H_∞control problem of a class ofsystems with time-varying delay is studied based on state feedback. First,for time-delay d (t)in two above cases, the H_∞performance of sys- tems with time-varying delay is analyzed by applying the above methods,and, new delay-dependent bounded real conditions are obtained, whichguarantee that the system is asymptotically stable. For the nonlinearterms of matrix inequalities, an improved cone complementary lineariza-tion (ICCL) algorithm is applied to make the Matlab simulation in thispaper, and the H_∞state feedback controller gain is obtained. Finally,Numerical example simulations are given to verify the feasibility andeffectiveness of the method in this paper.3) The delay-dependent robust stability and H_∞control problemof networked control systems with randomly varying delay and missingmeasurements are investigated by employing stochastic theory and time-delay systems approach. Then, new delay-dependent bounded real con-ditions are obtained, which guarantee that the networked control systemis asymptotically stable. For the nonlinear terms of matrix inequalities,the above ICCL algorithm is also used and the H_∞state feedback con-troller gain is finally obtained. Numerical example simulations are givento show that the method in this paper has certain superiority.