Lyapunov Function Design using Quantization of Markov Process
نویسندگان
چکیده
In this paper, we propose a Lyapunov function design method using a difference approximation scheme and quantization of the Markov process. First, we approximate a Lyapunov equation by a Schrödinger-like equation. Second, we obtain sufficient conditions for a function to be a Lyapunov function. Then, we provide a Lyapunov function design procedure.
منابع مشابه
Design of Observer-based H∞ Controller for Robust Stabilization of Networked Systems Using Switched Lyapunov Functions
In this paper, H∞ controller is synthesized for networked systems subject to random transmission delays with known upper bound and different occurrence probabilities in the both of feedback (sensor to controller) and forward (controller to actuator) channels. A remote observer is employed to improve the performance of the system by computing non-delayed estimates of the sates. The closed-loop s...
متن کاملDesigning an Economic Repetitive Sampling Plan in the Presence of Two Markets
In this paper, we develop an optimization model for the economic design of repetitive sampling plan in the presence of two markets. The process under consideration produces a product with a normally distributed quality characteristic with unknown mean and known variance. The quality characteristic has a lower specification limit. The quality of the product is controlled via lot-by-lot acceptanc...
متن کاملA Lyapunov view on positive Harris recurrence of multiclass queueing networks
In this paper we prove the positive Harris recurrence of the underlying Markov process of a multiclass queueing network. Using the fact that under certain conditions the stability of a fluid network is equivalent to the existence of a continuous Lyapunov function, we propose a new method to conclude that the underlying Markov process is positive Harris recurrent if the associated fluid network ...
متن کاملOn the construction of Lyapunov functions for nonlinear Markov processes via relative entropy
We develop an approach to the construction of Lyapunov functions for the forward equation of a nite state nonlinear Markov process. Nonlinear Markov processes can be obtained as a law of large number limit for a system of weakly interacting processes. The approach exploits this connection and the fact that relative entropy de nes a Lyapunov function for the solution of the forward equation for ...
متن کاملADAPTIVE BACKSTEPPING CONTROL OF UNCERTAIN FRACTIONAL ORDER SYSTEMS BY FUZZY APPROXIMATION APPROACH
In this paper, a novel problem of observer-based adaptive fuzzy fractional control for fractional order dynamic systems with commensurate orders is investigated; the control scheme is constructed by using the backstepping and adaptive technique. Dynamic surface control method is used to avoid the problem of “explosion of complexity” which is caused by backstepping design process. Fuzzy logic sy...
متن کامل