Robust H∞ control of discrete switched system with time delay
ABSTRACT This paper deals with the stabilization and robust H-infinity control of discrete switched system with time delay. The switching is time-driven and the design is based on the average dwell time method. The controller parameters and the permissible switching sequence, subject to the given average dwell time, can be obtained by solving a set of linear matrix inequalities (LMIs). Two examples are given to demonstrate the proposed methods.
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ABSTRACT: We consider a switching system composed of a finite number of linear delay differential equations (DDEs). It has been shown that the stability of a switching system composed of a finite number of linear ordinary differential equations (ODEs) may be achieved by using a common Lyapunov function method switching rule. We modify this switching rule for ODE systems to a common Lyapunov functional method switching rule for DDE systems and show that it stabilizes our model. Our result uses a Riccati-type Lyapunov functional under a condition on the time delay.Circuits and Systems I: Regular Papers, IEEE Transactions on 03/2006; · 2.24 Impact Factor
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ABSTRACT: We formulate a model for hybrid dynamical systems with delay, which covers a large class of delay systems. Under several mild assumptions, we establish sufficient conditions for uniform asymptotic stability of hybrid dynamical systems with delay via a Lyapunov-Razumikhin technique. To demonstrate the developed theory, we conduct stability analyses for delay sampled-data feedback control systems including a nonlinear continuous-time plant and a linear discrete-time controller.IEEE Transactions on Automatic Control 03/2003; · 2.72 Impact Factor
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ABSTRACT: Bistability, the capacity to achieve two distinct stable steady states in response to a set of external stimuli, arises within biological systems ranging from the lambda phage switch in bacteria to cellular signal transduction pathways in mammalian cells. On the other hand, more and more experimental evidence in the form of bimodal population distribution has indicated that noise plays a very important role in the switching of bistable systems. However, the physiological mechanism underling noise-induced switching behaviors remains to be fully understood. In this paper, we investigate the effect of noises on switching in single and coupled genetic toggle switch systems in Escherichia coli. In the case of the single toggle switch, we show that the multiplicative noises resulting from stochastic fluctuations in degradation rates can induce switching. In the case of the toggle switches interfaced by a quorum-sensing signaling pathway, we find that stochastic fluctuations in degradation rates inside cells, i.e., intracellular noises, can induce synchronized switching, whereas the extracellular noise additive to the common medium can not only entrain all the individual systems to switch in a synchronous manner but also enhance this ordering behavior efficiently, leading a robust collective rhythm in this interacting system. These insights on the effect of noises would be beneficial to understanding the basic mechanism of how living systems optimally facilitate to function under various fluctuated environments.BMC Systems Biology 02/2007; 1:50. · 2.98 Impact Factor