On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters

V. CONCLUSION In this note, we have considered the control of partially linear cascade nonlinear systems. We have given conditions under which switching of the gains of the linear controller can stabilize the cascade. Our condition, Assumption 1 for the existence of an invariance region is different than ISS and weaker than minimum phase assumptions. Of course, the tradeoff is that the switching policy depends on the state of both subsystems and that in general, only boundedness of trajectories is achieved. It would be of great interest to investigate the precise relationship between the conditions of this note and these other more familiar notions. For example, in the simulated system (27)–(29), the invariance condition (40) shows that the ratio k 2 =k 1 grows with the radius R of the invariance region G. The gains of a nonpeaking constant gain controller have this same property [1]. However, since the initial condition for z does not enter into that calculation we have more freedom in the design of the gains. It appears that the switching controller automatically adjusts the output gain to find a nonpeaking controller. Since the trajectories of the invariance controlled system are bounded by the prescribed invariance region one of the additional advantages of invariance control is that it may also be useful to enforce constraints on the states of the internal dynamics. There are many applications which require not only output regulation and internal stability but also that the internal states remain bounded below prescribed values. Further studies along these lines would also be valuable. Sufficient conditions for invari-ance control of a class of nonlinear systems, " in Proc. 39th IEEE Conf. Invariance control of normal forms with input driven internal dynamics, " in Proc. avoidance of steerable vehicles with invariance control, " in Proc. Intelligent switching control of nonlinear nonminimum phase relative degree two systems, " in Proc. Eu-Abstract—In this note, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all …