Researches On Stability And Feedback Control Of Dynamic Systems With Delay Based On Delay-Reconstructing Approach

The stability and control problems of dynamic systems with delay involving re-current neural networks with delay and linear delayed systems, have attracted much attention under development of intelligent, information, and networked techniques. At present, a zero-sum-based simple method is employed to reduce the conservatism of stability or control schemes. But there is still no discuss or result on the relation-ship between delay and stability or control of systems. The stability and control of recurrent neural networks with delay and linear delayed systems are studied in this dissertation, and the relationship between delay and stability or control of sys-tems is built directly. By reconstructing and recombining the delay and functional parameters, the new less conservative stability criteria and control scheme can be obtained. The main contributions of this dissertation are as follows:(1) The stability problem of recurrent neural networks with delay is studied. By using the idea of dividing delay interval, the several weighting delays can be constructed, and some less conservative delay-dependent asymptotic stability criteria are proposed for recurrent neural networks with delay, which can be called "weighting delay method". Then, the optimal weighting delay parame-ters and stability results can be obtained by designing an optimization process to calculate the proposed criteria.(2) A new class of switched neutral-type neural networks (SNTNNs) with delay is established by considering the neutral-type delay and the switching behavior in neural networks. A new series compensation scheme is proposed base on the characteristics of delay and augmented Lyapunov-Krasovskii functional, and the aim on adding some useful negative definite terms in the criteria is achieved. Thus, the robust stability criteria of SNTNNs with time-varying delays can be built by combining the series compensation scheme and aug-mented functional. Then, the case of fast varying neutral-type delay can be considered. Meanwhile, the corresponding robust stability result for switched recurrent neural networks with time-varying delay can be obtained.(3) The stability problem of recurrent neural networks with multiple delays is stud-ied. By reconstructing a new delay vector based on multiple delays, a more compact augmented recurrent neural networks can be proposed. Then, by constructing a line integral type Lyapunov-Krasovskii functional, the less con-servative stability criteria can be obtained. Next, by combining weighting delay and delay reconstructing, a new changeable delay vector can be estab-lished. The stability criterion can be obtained by employed line integral type Lyapunov-Krasovskii functional again. A theorem can prove that the proposed criterion is less conservative.(4) The global exponential stability of a class of fuzzy cellular neural networks with time-varying delays is studied. By transforming fuzzy weight matrices to non-fuzzy one, the signs of elements of the non-fuzzy terms'weight matrices is considered. The novel delay-dependent stability criterions based on linear matrix inequality (LMI) technique are derived. Then, by considering the case of fuzzy cellular neural networks with fuzzy and non-fuzzy term delays, the less conservative delay-dependent global exponential stability criterion can be obtained.(5) The stability of linear neutral system with time-varying retarded-type de-lay and time-varying neutral-type delay is studied. By employing an aug-mented Lyapunov-Krasovskii functional and a simplified series compensation technique, the less conservative stability criteria are obtained base on convex combination. And then, the non-fragile H? control problem for uncertain linear neutral system with delay is studied. On the basis of the proposed stability, the less conservative delay-dependent non-fragile H? control scheme are obtained.(6) The problem of static output feedback stabilization for linear systems with time-varying delay is studied. A matrix transformation method is proposed for static output feedback controller design, which is easier to be solved and realized, and leads to the better system performance. Then, the distributed static output feedback consensus problem is studied for multi-agent systems with time-varying delay. A new necessary condition on the consensusability of multi-agent systems is proposed to guarantee the exist of the admissible output feedback signal, and a new distributed static output feedback consensus protocol is designed.