Independent of delay stability criteria for uncertain linear state space models

About global asymptotic stability of dynamic systems with time lags and uncertainties within polytopes

“…Time-delay systems are very common in nature like, for instance, related to transportation problems, population growing, signal transmission, or neural network-based models (Niculescu, 2001;Brierley et al, 1982;Bourles, 1987;De la Sen, 1994Luo and van den Bosch, 1997;Chen, 1995;Gu, 1977;Xu, 1997Xu, , 2000De la Sen and Luo, 2003;Arik, 2003). The stability and stabilization of such systems has been widely studied in the literature in connection, for instance, with Lyapunov theory or frequency domain methods (see, for instance, Niculescu, 2001;Brierley et al, 1982;Bourles, 1987;De la Sen, 1994Luo and van den Bosch, 1997;Chen, 1995;Gu, 1977;Xu, 1997Xu, , 2000De la Sen and Luo, 2003 and references therein).…”

New results on linear parameter-varying time-delay systems

“…Also, in connection with system measurements and/or information flow amongst different parts of dynamical systems, time-delay arise quite naturally [7]. For a modest coverage of the recent results on the class of uncertain delay systems; see [8][9][10][11][12][13] and their references. A common conclusion drawn from the ensuing results is that time-delay has, by and large, a destabilizing effect on the control system.…”

“…In this paper, we consider a new class of time-delay systems which has not been studied before in the literature [7][8][9][10][11][12][13][14]. This class represents a linear parametervarying time-delay systems (LPVTD) where the state-space matrices depend on timevarying parameters and the time-delay is unknown but bounded.…”

Linear Parameter-Varying State-Delay (LPVSD) Systems: Stability and L2-Gain Controllers

“…In this article, we consider a new class of time-delay systems which has not been studied before in the literature [7][8][9][10][11][12][13]17]. This class represents a linear parameter-varying state-delay (LPVSD) systems where the state-space matrices depend on time-varying parameters and the time-delay is unknown but bounded.…”