Unified Approach to the Analysis and Performance Evaluation of Sampled-Data Control Applied to Nonlinear Systems ?

摘要

This paper presents a general and unified approach to the stability and performance analysis of Markov jump nonlinear systems governed by a state feedback sampled-data control law, where the sampling instants are evenly spaced. Initially, the closed-loop system is equivalently described as a hybrid system. Then, mean square stability and performance optimization of the general nonlinear hybrid system are addressed. This study is based on the existence of a solution of a Two-Point Boundary Value Problem (TPBVP) composed by a Hamilton-Jacobi-Bellman Equation (HJBE) and defined in the time interval corresponding to two consecutive sampling instants. Solving this TPBVP implies that the performance index of interest is exactly evaluated. Additionally, a numerical method is proposed to cope with theH2framework. In this case, a guaranteed upper bound to the referred index is obtained. Examples illustrates the proposed theoretical results.