Oscillation, Stability And Control Of Distributed Parameter Systems With Delays

Based on the oscillation theory of systems and Lyapunov stability theory, by using Green's formula, Gauss divergence theorem, nonsingular linear transformation, delay inequalities, assistant function, Lyapunov function as the main mathematical tools, the oscillation, asymptotic stability and variable structure control problems of distributed parameter systems with delays are discussed in this dissertation.The main contributions of this dissertation are as follows:1. Oscillation problems for delay parabolic systems, delay neutral parabolic systems and delay neutral hyperbolic systems are discussed respectively. Some necessary and sufficient conditions for oscillation of the solutions of Robin boundary problems of neutral distributed parameter systems with delays are obtained.2. First, Two nonexistence theorems for positive solutions of delay hyperbolic systems with impulses are established and their applications in oscillation theory of impulsive delay hyperbolic systems are studied. Second, this dissertation discusses oscillation of a class of delay neutral hyperbolic systems with impulses. And necessary and sufficient conditions for oscillation of the impulsive hyperbolic systems with delays are obtained.3. This dissertation establishes oscillation theorems for the partial difference systems with continuous variables and some examples are also analyzed.4. By making use of Lyapunov stability theory and delay inequalities as the main mathematic tool, the asymptotic stability for a class of sliding mode equations rising in distributed parameter control systems with time delays was investigated. Sufficient conditions of exponential asymptotic stability for the sliding mode equations with delays are found. Two theorems of the exponential asymptotic stability for the sliding mode equations are established. The results on the exponential asymptotic stability of the distributed parameter control systems with delays provided the theoretical foundation for the variable structure control...