On Robust Control Of Continuous-time Dynamic Systems With State-dependent Uncertainties

In aerospace, astronautics and other industrial fields, there exist a large structureduncertain systems. Variations of system parameters are closely dependent on the currentstate of the system. Such objects with uncertain parameters can be tunnel diode, negativeresistance oscillators or Josephson junction in electronic circuit systems; stifness, iner-tia, or viscosity coefcients in mechanical systems; aerodynamical coefcients in flightcontrol systems and so on. Therefore, it has important practical significance to study therobust control of the systems with the state-dependent uncertainties or nonlinearities. Themain content of this paper is about the analysis and synthesis of such special time-varyingsystems with state-dependent uncertainties.This thesis, on the basis of the existing research of systems with uncertain param-eters, systematically and deeply investigates the problems of robust control of dynamiccontinuous-time systems with state-dependent uncertainties, and presents analysis andsynthesis methodologies for uncertain dynamic systems with state-dependent in the uni-fied framework. Part of the research results are applied to tunnel diode circuit system,spring-damper system, and chaos supressibility, Synchronization control, and secure com-munication of chaotic system.Firstly, basic model, which requires that the uncertainties in state matrix and controlmatrix can be described by the same state-dependent parameter vector, is given for thecontinuous-time system with state-dependent uncertainties. Then, a more general poly-topic model describing systems with state-dependent uncertain parameters is proposed,and such a system model is more applicable in practice. In the rest paper, we focus onlyon the case where the uncertainty polytope of control matrix has the same number ofvertices as the uncertainty polytope of system matrix.Robust stability conditions for the considered uncertain systems are first establishedon the basis of common quadratic Lyapunov function (CQLF). Then, a novel non-quadraticparameter-dependent Lyapunov function is proposed, upon which, less conservative ro-bust stability conditions are derived. By introducing the Lagrange multiplier term andweight matrix variables, a low conservative stability condition is obtained for the contin-uous time system with state-dependent uncertainties. Dependent on the improved stability conditions, the static output controller is de-signed for the system. Then, the model-dependent output-feedback controllers are alsoformulated for such systems. Besides, a new controller design with the decay rate set inadvance is proposed, which have more flexibilities and can achieve the better system per-formances in practice. Numerical examples together with classic tunnel diode circuit andmass-spring-damper system are used to demonstrate the efectiveness and applicability ofour theoretical results.Based on the assumption of that behavior of chaotic system occurs in the finite-statespace, a classical example of Chua’s circuit is used to demonstrate the efectiveness andapplicability of the proposed robust controller design method for stabilization and syn-chronization control problem of chaotic system. A chaos secure communication system isconstructed based on the robust control method proposed which extends the robust controltheory for the continuous-time systems with state-dependent uncertainties and provides adesign example for practical engineer’s reference as well.