Dissipativity-Based Two-Dimensional Control and Filtering for a Class of Switched Systems

This paper deals with the dissipative control and filtering problems for the discrete-time two-dimensional (2-D) switched Fornasini-Marchesini (FM) systems. First, the definition of 2-D TSR- ϑ-dissipativity for the FM systems is introduced. By employing the switched quadratic Lyapunov function technique and establishing multiple recursive formulas, sufficient conditions are developed to guarantee that the considered system is asymptotically stable under the arbitrary switching signal (ASS) case and exponentially stable under the restricted switching signal (RSS) case with the 2-D TSR- ϑ-dissipativity, respectively. The special cases, such as the 2-D passivity performance and the 2-D H
_∞
performance, are also discussed. Based on the obtained dissipative stability conditions, the 2-D TSR- ϑ-dissipative state feedback controller and filter design problems are further studied for the addressed system. Particularly, the extended average dwell time (define this later on in text) technique is utilized for the system under the RSS case. Finally, the effectiveness of the proposed design method is illustrated by numerical examples.