On Key Theoretic Problems For A Large Class Of Time-Delay Systems

A large class of time-delay systems investigated in this paper includes the specific time-delay systems such as neutral constant and time-varying delay-differential systems and Markov random delay systems and the generalizing time-delay systems such as neutral functional constant delay-differential systems and fractional-order abstract neutral delay systems in Banach state spaces. Stability and controllability problems of the above time-delay systems have been investigated systematically in the present paper. Main contributions are as follows.1. Asymptotic stability analysis of linear neutral constant delay-differential systems is under investigation. From a novel point of view of matrix Lie algebra solvability, employing the frequency-domain method of characteristic equations and spectral radius of system matrices, delay-independent asymptotic stability criteria that are easy to check and computable are derived which are applicable to the case under which sufficient criteria of neutral root chain that accumulates to the imaginary axis not existing in open left half of complex plane are not satisfied, which verifies that asymptotic stability of linear neutral constant delay-differential systems remain checkable under the circumstances that system matrices space forms a solvable matrix Lie algebra and hence complements the theory about the study of stability for linear neutral constant delay-differential systems by the frequency-domain method of characteristic equations.2. Robust stability of linear neutral time-varying delay-differential systems with time-varying structured uncertainties has been dealt with based on LMI and using the method that one quadratic integral term together with Leibniz-Newton formula is added to the upper-bound estimation for time derivative of Lyapunov-Krasovskii functional. The quadratic integral term presented in this paper are often ignored in the literature where stability problem of neutral time-varying delay-differential systems has been investigated and thus delay-dependent and delay-derivative-dependent/independent stability criteria derived in this paper provide larger upper bound of time-delay guaranteeing the asymptotic stability of systems, which implies less conservativeness than those in the literature.3. Using first-order approximation stability theory, frequency-domain method of characteristic equation and matrix theory, real stability radius analysis problem of neutral constant delay-differential systems with nonlinear state has been investigated under real matrix perturbation for which computable formula is derived and numerical computation of the corresponding formula is carried out using golden separation search algorithm. Furthermore, the relation between real stability radius and time-delay is analyzed and hence it is shown by numerical example that real stability radius of nonlinear delay-differential systems does not monotonically decrease with delay increasing as in the case of linear delay systems of retarded and neutral types.4. Delay-dependent and delay-derivative-dependent sufficient conditions for existence of mode-independent exponential controller for continuous-time stochastic latency networked control systems (NCS) with non-accessible jumping modes are derived based on mode-dependent Lyapunov-Krasovskii functional and using the least conservative descriptor model transformation method and Moon's integral inequality bounding technique for cross product terms together with Dynkin formula in terms of LMIs, which are extended to the case of time-varying structured uncertainty and then demonstrates by numerical simulation the validity of such controller design method and thus solves the state-feedback control synthesis problem under the circumstances that sensor and controller have no access to the associated Markov state change relevant to failures of non-critical components.5. For linear uncertain neutral functional constant delay system as the generalization of linear neutral constant delay system, in terms of unstable region of bounded rectangular, using the system matrix function norm defined by bounded variation of system matrix function, robust stability criteria of norm-bounded uncertain functional systems are established which in a nontrivial way generalizes the stability results related to linear neutral multiple delay systems in the literature. Next, Variation-bounded uncertainty notion is proposed which is a novel uncertainty notion unique to neutral functional delay systems as opposed to norm-bounded and polytopic uncertainties notion in the case of specific neutral delay systems. Using the spectral radius of nonnegative matrix formed by bounded variation of system matrix function, robust stability criteria of variation-bounded uncertain functional systems are derived whose special criteria parallel to the stability results related to linear neutral single delay systems in the literature. Computation demonstrates the stability criteria presented in this paper provide larger upper bound of time delay and robust interval of system parameter guaranteeing asymptotic stability of linear neutral functional systems, which is less conservative than and hence makes an improvement over the results in the literature.6. In addition to linear neutral functional constant delay systems, neutral functional constant delay systems with nonlinear state are also considered for which stability criteria are established using the spectral radius of nonnegative matrix formed by bounded variation of system matrix function, first-order approximation stability theory, frequency-domain method of characteristic equation which in a nontrivial way generalize the stability results related to neutral constant delay systems with nonlinear state in the literature and are valid as shown in numerical example.7. Investigation of controllability for infinite-dimensional abstract time-delay systems as more general time-delay system is only limited to integral-order infinite-dimensional system so far. Controllability of fractional-order abstract impulsive neutral functional and evolution integro-differential systems with infinite delay has been initially investigated whose criteria have been established using fractional calculus, semigroup of operators, resolvent operators and Krasnoselskii fixed point theorem. Since operator has multi-valued mapping property, controllability of fractional-order abstract impulsive neutral functional integro-differential inclusions with infinite delay as more general abstract time-delay system has also been initially investigated whose criteria have been established using Leray-Schauder multi-valued fixed point theorem. In addition to infinite delay, controllability of fractional-order abstract impulsive neutral evolution integro-differential inclusions with state-dependent delay has also been initially investigated whose criteria have been established using weighted phase space and Dhage multi-valued fixed point theorem, which complements theory about controllability of abstract systems in Banach spaces.Finally, research work presented in this dissertation has been concluded systematically and further research aspect is pointed out.