An Elimination Theory for Differential Algebra by A Seidenberg

By A Seidenberg

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Ai+1 Ai x(ks ) = Υi x(ks ) and Vi (x(kv )) = xT (kv )Pi x(kv ) = (Υi x(ks ))T Pi Υi x(ks ). 3 is satisfied. 12). 9, it is clear that when the switching signals are arbitrary, Υi is unavailable, which indicates that the general MLF approach is inapplicable to conduct the stability analysis for the switched system under arbitrary switching. 4), it can be seen that for the underlying MLF, the approach does not require the comparison between the Lyapunov function values at two consecutive switching instants, and instead, requires the comparison between the Lyapunov function values at two neighboring switching instants.

SIAM J. Control Optim. 45(5), 1915–1930 (2006) 84. : Stability and stabilization of discrete time switched systems. Int. J. Control 79(7), 719–728 (2006) 85. : Stability and L2 -gain analysis for switched delay systems: a delaydependent method. Automatica 42(10), 1769–1774 (2006) 86. : New approach to stabilisation of networked control systems with timevarying delays. IET Control Theory Appl. 2(12), 1094–1104 (2008) 87. : On switching H∞ controllers for a class of linear parameter varying systems.

3) The corresponding MLF is called weak Lyapunov function. 3), allowing the value of the weak Lyapunov function to increase during the running time of each subsystem, the stability criterion is less conservative. However, the rising amplitude h of Lyapunov function value during the running time of each 30 2 Stability and Stabilization subsystem is hard to be determined, then it is difficult to derive an easily-checked stability criterion, even though the switched system without any complex dynamics, such as uncertainties, time delays.

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