Abstract
This paper is concerned with the problems of stability and -gain analysis for 2D (two-dimensional) discrete switched systems with time-varying delays described by the second FM state-space model. Firstly, we introduce the definition of the average dwell time for a 2D discrete switched system, which is an extension of the ‘average dwell time’ concept of a 1D (one-dimensional) switched system. Secondly, based on the average dwell time approach, delay-dependent sufficient conditions for the existence of the exponential stability for the 2D discrete switched system are derived and -gain performance for the considered system is also analyzed. All the obtained results are formulated in a set of LMIs (linear matrix inequalities). Finally, a numerical example is given to illustrate the effectiveness of the proposed results.
Highlights
D (Two-dimensional) systems, which are a class of multi-dimensional systems, have received considerable attention over the past few decades due to their wide applications in many areas such as multi-dimensional digital filtering, linear image processing, signal processing, and process control [ – ]
It is known that modeling uncertainties and disturbances are unavoidable in practical systems, and it is important to investigate the problems of H∞ control and robust stabilization of D systems
Because time delays frequently occur in practical systems and are often the source of instability, the H∞ control problem for a class of D discrete systems with state delays has been investigated in [, ]
Summary
D (Two-dimensional) systems, which are a class of multi-dimensional systems, have received considerable attention over the past few decades due to their wide applications in many areas such as multi-dimensional digital filtering, linear image processing, signal processing, and process control [ – ]. We are interested in investigating the issues of the exponential stability and l -gain analysis for D discrete switched systems with time-varying delays represented by the second FM model. In what follows, based on the extended average dwell time concept, we will investigate the problems of stability and l -gain analysis for a D discrete switched system with time-varying delays. It should be noted that we have studied the problems of stability analysis and stabilization of delay-free D switched systems using the average dwell time approach in [ ]. Remark Similar to the D switched system case, Definition means that if there exists a positive number τa such that the switching signal σ (i, j) has the average dwell time property, the average time interval between consecutive switching is at least τa. According to Definition , system ( ) is exponentially stable under the average dwell time scheme ( )
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