Robust Stability Analysis And Control Of Some Classes Of Systems With Time-varying Delays

Stability is one of the elementary structure properties of dynamical systems. The existences of uncertainty and time-delay may result in the instability of a sta-ble system. Therefore, the problems of robust stability and controller design for delay systems are hot issues in control theory. Now, there have been many results on the research of stability analysis and controller design for various uncertain sys-tems with delays. However, there exist few results on large-scale interconnected systems, descriptor systems and neutral systems with multiple time-varying delays and multiple uncertainties. By Lyapunov stability theory, matrix analysis theory and linear matrix inequality(LMI) technique, this thesis investigates the problems of stability analysis and controller design for large-scale interconnected systems, descriptor systems, interconnected descriptor systems, neutral interconnected sys-tems and nonlinear neutral systems with multiple time-varying delays and multiple uncertainties. The main results are summarized as follows:(1)The problem of the reliable guaranteed cost control is investigated for a class of uncertain large-scale interconnected systems with time-varying delays. The model of actuator failure covers normal operation, partial degradation and outage. The cost function is given in terms of integral quadratic function containing failure input. Utilizing Lyapunov approach and LMI technique, a sufficient condition for the existence of reliable guaranteed cost controller is derived. A numerical example is presented to demonstrate the design of guaranteed cost controller.(2)The problem of stability is studied for a class of uncertain descriptor systems with time-varying delays. The uncertainty is norm-bounded and the delay belongs to an interval. By introducing some matrix variables, a delay-dependent stability criterion which is applicable to both fast and slow time-varying delay cases is pro-posed. Compared with the existing results, the obtained method admits a larger feasible area and a larger upper bound for the time-varying delay.(3)The observer-based robust H∞control problem is investigated for a class of uncertain interconnected descriptor systems with time-varying delays. All of the system state matrix, control input matrix and interconnection coefficient matrix contain uncertainties and time-varying delays exist in system state, control input and interconnection. Utilizing the scheme of partially counteracting the intercon-nections, a design approach for the H∞controller based on observer is given in terms of LMIs.(4)The problems of the non-fragile decentralized guaranteed cost control and optimization are studied for a class of uncertain neutral interconnected systems composed by N subsystems. By magnifying the cross terms(the product of inter-connection and some coefficient matrices), the design problem of the non-fragile decentralized guaranteed cost controller is reduced to the feasibility problem of N coupled matrix inequalities. Only one of these matrix inequalities is LMI. An al-gorithm which can deal with the nonlinear constraints is proposed to solve the optimization problem of the guaranteed cost. Two examples are given to illustrate the design approach. The minimization of the guaranteed cost by this method is less than those obtained by the existing results.(5) The problems of the non-fragile decentralized guaranteed cost control and optimization are investigated for a class of neutral interconnected systems with un-certainty in interconnection. By introducing some new matrix variables and mag-nifying appropriately the guaranteed cost, a convex optimization object subject to LMIs is obtained. Then a guaranteed cost controller design method is given in terms of LMIs. In this method, the interconnection is viewed as effective information, not disturbances and the cross terms are not magnified.(6)The descriptor system approach is applied to the investigation on the guar-anteed cost controller design and optimization for uncertain neutral interconnected systems and nonlinear neutral systems. Guaranteed cost controller design methods are given in terms of LMIs for the two classes of systems. The methods depend on the derivatives of time-varying delays, not the sizes of the time-varying delays. For the guaranteed cost optimization problems of the two classes of systems, con-vex optimization objects are obtained by introducing constant and matrix variables, respectively. The obtained methods are less conservative than the existing results.