Robust H_∞ and Guaranteed Cost Control for Jump Linear Systems with Time Delay

Abstract

The linear Markov jump model that is usually used in the analysis and design phases is an approximation of a real nonlinear system with Markov jumps in the neighborhood of the operating point. For many reasons well known in the control community, the systems parameters and the operating point change with time and therefore, the fixed linear Markov jump model is not adequate to guarantee robustness of system performance. Besides this, the system can be affected by exogenous disturbances, which will make the degradation worse. To overcome this surprise, the control engineer should take care of these uncertainties and exogenous disturbances during the analysis and design phases to guarantee the required stability and other system performance, despite the presence of uncertainties in the system. The results presented so far for the class of linear systems with Markov jumps and time delay are not adequate to guarantee the robustness of the desired performance. The robust H∞ control problem was developed to maintain robustness of stability and performance when it known algorithms lack robustness, that is, the system parameters have uncertainties. This chapter deals with the robust H∞ control and the guaranteed cost control problems for jump linear systems with norm-bounded uncertainties and time delay. The rest of the chapter is organized as follows.we deal with the robust H∞ control problem. considers he guaranteed cost control problem. we cover the output feedback guaranteed cost control problem.