Research On Robust Stabilization And Stabilization Design Of Nonlinear Systems Based On Dissipative System Theory

For recent years, although a great many important results have been achieved in the field of robust stabilization and stabilization design of nonlinear systems based on dissipative system theory, many researches remain to be done. In this dissertation, on the one hand, we reinforce or improve some theoretic results, on the other hand, by using theorems existed or developed in this dissertation, we pursue the researches on robust stabilization and stabilization design in diverse complex nonlinear systems. The contributions of this dissertation consist of the following:1.Passivity theory is an important component of dissipative system theory, we investigate its applications to robust stabilization and stabilization design. Non-affine nonlinear systems via bounded controls and Kalman-Yakubovitch -Popov lemma of affine passive systems are stabilized. Several kinds of nonlinear systems with uncertainty by using stability theory of cascaded passive systems are stabilized robustly. The relative weaker sufficient conditions of stabilizing a class of driven-driving systems by using the concept of zero-state-detectability are put forward.2.1nput-to-state stable theory is a new area of dissipative system theory, we propose some theoretic results and investigate their applications. A new characterization of input-to-state stability which is beneficial to input-to-state stabilization design is presented. A nonlinear small-gain theory with which input-to-state stable theory becomes a more effective analysis tool of stabilization design is put forward.3.We investigate the function of passivity theory in input-to-state stabilization. The usual precondition guaranteeing input-to-state stabilization by exploiting the concept of zero-state-detectability is weakened, and a class of linear systems subject to saturation by using the results above is input-to-state stabilized. 4.The decisive function of control Lyapunov functions in robust stabilization and stabilization design is studied. Since Sontag-Type control based on controlLyapunov function is an important control law in robust stabilization of affine systems, we point out that is a kind of variable structural control in essence. Due to this recognition and the fact that control Lyapunov functions are difficult to be constructed, we propose the concept of weak control Lyapunov function and then prove the stabilizing property and the robustness of Sontag-Type control. Using the way of proposing the control Lyapunov function and the special structure of Sontag-Type control, we investigate the dissipassivation control of a kind of perturbed nonlinear systems. The applications of homogeneity theory to stabilization design based on control Lyapunov functions are studied and some new results are obtained.5.The function of weak Lyapunov functions in stabilization design is studied. We characterize a kind of globally asymptotically stable systems which have only semi-definite positive weak Lyapunov function. Based on this characterization, we improve the theoretic result which is the foundation of Lyapunov backstepping design. The problem that how to construct a control Lyapunov function from a weak Lyapunov function is a significant one, because the successful reconstruction implies that robust analysis and design can be probed in depth. For affine nonlinear systems, we present a sufficient reconstruction condition and interpretate the constructing procedure by typical examples.6.Nonlinear H-infinite control based on Lp(p l) gain stability is being extensively investigated recently. We present a theoretic result, i.e., put forward an inequality approach, which is different from the usual differential game method, to estimate the best control and the worst disturbance.