Analysis And Design Of Delay-dependent Stability For Network-based Systems Via Convex Combination

So far, works on stability analysis and synthesis of time-varying delay systems mainly employ Leibniz-Newton (L-N) formula and free weighting matrices to reduce conservatism of model transformation methods. However, free matrix method re-quires excessive introduction of weight matrices, making calculational amount much large. Through adopting Jensen's inequality and Wirtinger's inequality, the author investigates the delay dependent stability related problems of time delay systems, and the corresponding computational complexity of previous methods is consider-ably lessened. Meanwhile, several convex combination techniques can reduce the conservativeness induced by solely using Jensen's inequality during inequality scal-ing, and avoid the curse of dimensionality caused by the delay division method popularized recently. The proposed new convex combination based methodology is applied successfully to stability, stabilization of network-based systems and their control problems. The results obtained in this work are less conservative condition-ally and expensive computationally. The main research of the dissertation can be briefly described as follows:1. The robust resilient control problem is investigated for uncertain networked control systems (NCSs) with variable sampling intervals, variant induced de-lays and possible data dropouts, which is seldom considered in current litera-ture. It is mainly based on the continuous time-varying-delay system approach. Followed by the nominal case, delay-dependent resilient robust stabilizing con-ditions for the closed-loop NCS against controller gain variations are derived by employing a novel Lyapunov-Krasovskii (L-K) functional which makes good use of the information of both lower and upper bounds on the varying input delay, and the upper bound on the variable sampling interval as well. A feasi-ble solution of the obtained criterion formulated as linear matrix inequalities can be gotten. A tighter bounding technique is presented for acquiring the time derivative of the functional so as to utilize many more useful elements, meanwhile neither slack variable nor correlated augmented item is introduced to reduce overall computational burden.2. The problem of delay-dependent adaptive reconfigurable controller design a-gainst unknown actuator faults is studied for linear continuous systems with time-varying delay. Based on the on-line estimation of possible faults by dis-continuous adaptation law, identification parameters of the adaptive state feedback controller are updated autonomously to compensate the fault ef-fects on the delayed system. For the first time, a convex combination idea and a projection-type adaptive approach are combined organically to derive the main results. A set of new delay dependent reconfigurable stabilization criteria, which guarantee the stability of closed-loop systems in both fault-free and faulty cases, are established in terms of linear matrix inequalities. The linearized model for the lateral motion of Boeing 747 is simulated to illustrate the superiority and the effectiveness of the presented adaptive delay-dependent results.3. The relaxed stabilization problem is considered for a class of nonlinear NCSs under variable sampling with variant state and network delays. An equivalent continuous-time uncertain fuzzy system with both state and input time vary-ing delays is derived based on the Takagi-Sugeno (T-S) model and the input delay method. In order to obtain much less conservative results for the delay system transformed, a more relaxed stabilizability condition of a delay-free T-S system and a tighter bounding lemma for some derivative terms of the constructed functional are utilized for closed-loop stability determination of the NCS under variable sampling. Delay-dependent stabilization conditions formulated in terms of linear matrix inequalities for the network-based system are derived by employing a novel L-K functional, which makes good use of the information of both the lower and upper bounds on the two interval delays.4. A fault-tolerant variable sampling control (VSC) scheme is developed for a class of nonlinear NCSs with time-varying state and random network delays. An uncertain continuous T-S fuzzy system with both state and input vary-ing delays, in the presence of possible actuator faults, is obtained equivalently on the basis of the input delay methodology. A tighter bounding lemma is proposed so as to gain less conservative closed-loop stability criteria. Delay-dependent conditions in terms of linear matrix inequalities are derived for the mode-independent fault-tolerant stabilizing controller of the resulting Marko-vian network-based system by employing a novel stochastic L-K functional.5. The problem of sampled-data control is investigated for T-S fuzzy systems with aperiodic sampling intervals based on an enhanced input-delay approach. Delay-dependent stability and stabilizability conditions for the closed-loop continuous nonuniformly sampled-data fuzzy systems are derived by construct-ing a novel discontinuous L-K functional which makes good use of not only the upper bound on the variable sampling interval, but also of its sawtooth struc-ture information about varying input delay which is often ignored in previous results. A bounding technique combined by reciprocally convex technics and linear convex combination is presented for acquiring the time derivative of the functional, wherein Jensen's inequality and Wirtinger's inequality are integra-tively employed. And a feasible solution of the obtained criterion formulated as parameterized linear matrix inequalities is ultimately conceived.6. A novel method is proposed for the stability problem of a class of recurrent networks with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for local-field and static neural networks with time-varying delay are respectively derived by the newly proposed aug-mented simple L-K functional. Different from previous results by using the first order convex combination property and L-N formula, our derivation applies the idea of second order convex combination, and the property of quadratic convex function which is given in the form of a lemma without resorting to the Jensen's inequality. Numerical examples are provided to verify the effec-tiveness and superiority of each presented results.