Robust Stability Analysis And Control Of Some Classes Of Systems With Timevarying Delays  Posted on:20100327  Degree:Doctor  Type:Dissertation  Country:China  Candidate:H L Hu  Full Text:PDF  GTID:1228330371950136  Subject:Control theory and control engineering  Abstract/Summary:  PDF Full Text Request  Stability is one of the elementary structure properties of dynamical systems. The existences of uncertainty and timedelay may result in the instability of a stable 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 systems with delays. However, there exist few results on largescale interconnected systems, descriptor systems and neutral systems with multiple timevarying 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 largescale interconnected systems, descriptor systems, interconnected descriptor systems, neutral interconnected systems and nonlinear neutral systems with multiple timevarying 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 largescale interconnected systems with timevarying 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 timevarying delays. The uncertainty is normbounded and the delay belongs to an interval. By introducing some matrix variables, a delaydependent stability criterion which is applicable to both fast and slow timevarying delay cases is proposed. Compared with the existing results, the obtained method admits a larger feasible area and a larger upper bound for the timevarying delay.(3)The observerbased robust H∞control problem is investigated for a class of uncertain interconnected descriptor systems with timevarying delays. All of the system state matrix, control input matrix and interconnection coefficient matrix contain uncertainties and timevarying delays exist in system state, control input and interconnection. Utilizing the scheme of partially counteracting the interconnections, a design approach for the H∞controller based on observer is given in terms of LMIs.(4)The problems of the nonfragile 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 interconnection and some coefficient matrices), the design problem of the nonfragile decentralized guaranteed cost controller is reduced to the feasibility problem of N coupled matrix inequalities. Only one of these matrix inequalities is LMI. An algorithm 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 nonfragile decentralized guaranteed cost control and optimization are investigated for a class of neutral interconnected systems with uncertainty in interconnection. By introducing some new matrix variables and magnifying 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 guaranteed 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 timevarying delays, not the sizes of the timevarying delays. For the guaranteed cost optimization problems of the two classes of systems, convex optimization objects are obtained by introducing constant and matrix variables, respectively. The obtained methods are less conservative than the existing results.  Keywords/Search Tags:  largescale interconnected systems, descriptor system, interconnected descriptor systems, neutral interconnected systems, nonlinear neutral system, model of actuator failure, reliable control, interval timevarying delay, observerbased H_∞control  PDF Full Text Request  Related items 
 
