Unified Approach to the Analysis and Performance Evaluation of Sampled-Data Control Applied to Nonlinear Systems⁎. Issue 25 (2018)

• Record Type: Journal Article
• Authors: Gabriel, Gabriela W.; Geromel, José C.
• Is Part Of: IFAC-PapersOnLine. Volume 51:Issue 25(2018)
• Page Start: 216
• Page End: 221
• Publication Date: 2018
• Subjects: Sampled-data control systems -- nonlinear systems -- optimization problems -- Markov parameters; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2018.11.108
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: 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 the H 2 framework. In this case, a guaranteed upper bound to the referred index is obtained. Examples illustrates the proposed theoretical results.