Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This note is concerned with stability analysis and stabilization of randomly switched systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and beten two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure stability and stability in the mean using Lyapunov-based methods when individual subsystems are stable and a certain ldquoslow switchingrdquo condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur beten the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous-time Markov chains; our results, therefore, hold for Markovian jump systems in particular. For systems with control inputs,  provide explicit control schemes for feedback stabilization using the universal formula for stabilization of nonlinear systems.
['Debasish Chatterjee', 'Daniel Liberzon']
I am writing a research paper on a idea On Stability of Randomly Switched Nonlinear Systems
[{"from": "human", "value": "I am writing a research paper on a idea On Stability of Randomly Switched Nonlinear Systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This note is concerned with stability analysis and stabilization of randomly switched systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and beten two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure stability and stability in the mean using Lyapunov-based methods when individual subsystems are stable and a certain ldquoslow switchingrdquo condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur beten the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous-time Markov chains; our results, therefore, hold for Markovian jump systems in particular. For systems with control inputs,  provide explicit control schemes for feedback stabilization using the universal formula for stabilization of nonlinear systems."}]