Study On Static Output Feedback Sliding Mode Control Algorithms

In recent years, sliding mode control has been paid more attentions and become an important branch of nonlinear control theory, because of its prefect features of arbitrary robustness and complete adaptation to matching uncertainties and outside disturbances. As the theory of sliding mode control is built on the state space, most of the extant results are relied on the state feedback and there are few results based on the output information. Motived by this, this dissertation deeply addresses the problem of static output feedback sliding mode control (SOFSMC). The main contributions are described as following:I). The basic problems of SOFSMC, existence problem of sliding surface and synthesis problem of control law, are explored for the nominal system. Different to the previous results of the existence problem needing complex coordinates transformation and appealing to static output feedback stabilization problem, two novel methods are proposed to solve the existence problem. One is structural Lyapunov matrix method. This method requires a somewhat simple coordinates transformation, under which it is discovered that the solution of the existence problem should satisfy some special structure. An optimal method is developed subsequently on the technique of linear matrix inequality (LMI) to obtain the permissible structure, and then get the ultimate solution of existence problem of SOFSMC. The other is the iterative linear matrix inequality (ILMI) method. Only original system parameters are involved in this method and the coordinates transformation is not utilized any more. So the procedure of SOFSMC design is simplified. More importantly, the results of robust SOFSMC can be easily extended on the ILMI method. For the synthesis problem of SOFSMC, two extant methods, assistant dynamic method and high gain method, is improved. The constraint of the former that the eigenvalues of the sliding motion system should differ from each other, is relaxed by the using a Lyapunov function. The corresponding optimal design is also proposed. For the latter, we present a concept of unitizing the norm of sliding matrix to optimize the control law design such that the control cost is limited.II). A robust SOFSMC design method is presented on the ILMI approach for a class of systems with parameter matrix uncertainties. Two special cases are discussed. One is the square system. A simple LMI result is made, which is also the LMI judge of robust minimum phase of the square system. The other is recently developed sliding surface matching condition. The conclusion of sliding surface matching condition of SOFSMC is presented. But it is very difficult to solve directly, even the ILMI is no longer effective. In such case, we prove that using the developed ILMI, the solution of sliding surface matching condition of SOFSMC can be indirectly obtained if it exists.III). We also primary explore the SOFSMC problem of systems with uncertain output information. In this dissertation, two cases under strong condition are explored. One is the output matrix uncertainties satisfying some condition. A LMI result is concluded. The other is output vector uncertainties satisfying sliding surface matching condition. The ILMI result is made and the corresponding system dynamics is completely immune to the output information uncertainties.IV). It is somewhat surprising that we find that the design problem of sliding mode observer is equivalent to the SOFSMC design with the input matrix being design parameter. So on the research of SOFSMC, the design of sliding mode observer for a class of system satisfying some positive real condition is discussed such that the linear feedback of sliding mode observe can be thought as linear quadratic Gaussian (LQG) optimal observer and the nonlinear feedback can be thought as the minimizing control cost design. In contrast to previous results, only original system parameters are involved here, so the method developed in this dissertation is simple and easily tractable. We also pointed out the linear feedback part and nonlinear feed...