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Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems by Xiaojie Su, Peng Shi, Ligang Wu

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2State Estimation and SMC of Markovian Jump Singular Systems

2.1 Introduction

In this chapter, we are aiming at the investigation of state estimation and SMC problems for Markovian jump singular systems. Although there has been some existing work on the stability analysis of such systems based on the LMI technique, the results are not all of strict LMI form since there are usually some matrix equality constraints. This may cause a lot of trouble in checking the analysis results numerically. Therefore, a natural question is immediately raised: are there any techniques that can release the matrix equality constraints? In this chapter, we extend the approach proposed in [195] to the stability analysis of Markovian jump singular systems, and a new necessary and sufficient stability condition is established in terms of strict LMI. Also, the analysis and synthesis of singular systems have been extensively investigated in the past decades, but little progress has been made toward solving the SMC problem of singular systems. This problem may become difficult and complicated due to the singular matrix E in the systems. Since the rank of E may not be equal to that of B in a simple singular LTI system of , it is difficult to obtain the so-called ‘regular form’ through conventional model transformation approach. As a result, the linear sliding surface is not suitable for singular systems. ...

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