Hybrid impulsive control for switched singular systems

Exponential stability of hybrid switched nonlinear singular systems with time-varying delay

“…Concerning the comparison with other well-known results in the literature [35][36][37][38][39][40], all these results have been presented for singular systems without considering simultaneously average dwell-time, time-delay, and nonlinear terms. Therefore, it is interesting and challenging to investigate the stability problem of switched nonlinear singular time-delay systems.…”

“…So arÀ1= 2h 2 ð Þ ln 1Àd À Á e À2ah 2 =1 þ max i Z i 3 Þ À and an estimation for upper bound for the maximum decay rate l is l max ¼ À1= 2h 2 ð Þln 1Àd À Á e À2ah 2 = 1 þ max i Z i 3 À Á ÞÀ ln s=T a À Á À . (ii) In Theorem 1 ''sufficiently large'' means that DZJNJf M þ M À Á g in which M and M were defined in (37) and (38). (iii) By letting Q sðtÞ 3 22 ¼ I, if (6a) and (6b) hold, then we can conclude that T a Z ln m=a À Á .…”

“…Owing to switches among multiple singular subsystems, it is inevitably difficult to analyze and synthesize such systems. There are some papers which have presented stability analysis of the switched singular system [35][36][37][38][39][40], but the simultaneous presence of switching signals with average dwell-time, time-delay, and nonlinearities have not been fully investigated. However, to the best of our knowledge, the delay range-dependent stability problem for switched nonlinear singular time-delay systems has not been fully investigated yet, which will be challenging due to the difficult extension of the existing stability results and has motivated us to carry out the present study.…”

H∞ Control with Transients for Singular Systems

“…Notice that singular system (2) is impulse-free if and only ifĀ 22 is invertible. Then, under an impulse-free condition, a consistent initial condition of singular system (2) is characterized as follows:…”

“…Before giving the controller design method, a sufficient condition guaranteeing the general excitation performance of closed-loop system (22) to be less than a prescribed positive scalar can be obtained by applying the LMIs in (8)- (10) of Theorem 2, in which Φ is replaced by QΛ T with P = P T , Q unknown, that is, the following two LMIs hold:…”