Research On The Dissipativity And Passivity Of Uncertain Systems

Dissipativity and passivity theories have been the focuses in control community, due to their wide applications in systems control and engineering problems. In the light of these recent studies in the fields, this dissertation provides a systematic study in robust dissipativity and passivity synthesis problems of nonlinear systems and linear time-delayed systems. Meanwhile, in the framework of dissipativity theory, almost disturbance decoupling with internal stability problem and nonlinear H_∞ control problem are also addressed. Some new design techniques are proposed and several new results are obtained. The major contents in this dissertation are as follows:1, The problem of adaptive feedback passification of a class of nonlinear systems with uncertain parameters is studied. Combining backstepping methodology with speed-gradient technique, the adaptive controller and the corresponding parameter update law are obtained, which render the closed-loop systems passive from new input to output.2, The robust passivity synthesis problem is concerned for a class of affine nonlinear systems with bounded-norm uncertainties. Firstly, based on the nonlinear matrix inequality (NLMI) approach, the sufficient conditions under which the unforced uncertain systems are robustly passive are derived; and then, again applying NLMI approach, the solvable conditions for the problem at hand are proposed, and the parameterized state feedback controllers are explicitly expressed.3, The robustly dissipative synthesis problem is discussed for a class of affine nonlinear uncertain systems with input-output feedthrough. Uncertainties appear in the vector field which multiplies the control. Firstly, based on Hamilton-Jacobi-Issacs (HJI) inequality approach, the sufficient condition under which the unforced systems are robustly dissipative is proposed; based on the former result, the solvable condition for the robustly dissipative control problem is obtained, and the corresponding state feedback controller is explicitly designed.4, The inverse optimal stabilization problem of a class of single-input non-affine nonlinear systems with nonlinear-nonquadratic performance index is firstly addressed, and the parameterized inverse optimal controllers are designed. Secondly, when the systems are dissipative, the inverse optimal control problem is discussed in the...