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               APPENDIX
               Proof of Theorem 1: The following Lyapunov-Krasovskii functions are well constructed

                                                                              (  )]                    (17)
                                          (  ) =       (  ) +       1  (  ) +       2  (  ) +       1  (  ) +       2
               where

                         
                     (  ) =    (  )    (  )
                       ∫    
                                     (  )   1   (  )    
                  (  ) =       2  (  −  )   
                     1
                          −     
                       ∫
                           −     
                                      (  )   2   (  )    
                  (  ) =        2  (  −  )   
                     2
                          −     
                         ∫   ∫
                            0     
                                       ¤    (  )   1 ¤(  )        
                  (  ) =            2  (  −  )       
                     1
                          −         +  
                               ∫     ∫    
                                  −     
                                               ¤    (  )   2 ¤(  )        
                  (  ) = (      −       )     2  (  −  )       
                     2
                                 −         +  
               By differentiating the above designed functionals along with   (  ), we can obtain
                          
                ¤
                     (  ) = 2   (  )  [    (  ) +       (   −   (  ))
                    −       (      ℎ) +     (  )]                                                      (18)
                ¤                    
                     1  (  ) = −2        1  (  ) +    (  )   1   (  )
                     −    −2                                                                           (19)
                               (   −       )   1   (   −       )
                                        ¤            (  ) +    −2          
                                             2  (  ) = −2        2     (   −       )   2   (   −       )
                                             −    −2                                                   (20)
                                                       (   −       )   2   (   −       )

                                      
                ¤                  2        
                                    
                     1  (  ) = −2        1 (  ) +    ¤ (  )   1 ¤(  )
                         ∫    
                                    ¤    (  )   1 ¤(  )    
                     −           2  (  −  )                                                            (21)
                            −     
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