Conditions for essential instability and essential destabilization of linear stochastic systems

Serving as a great supplement for stochastic stability and stabilization, new notions called essential instability and essential destabilization are introduced. In this way, according to the spectral distribution of an uncontrolled linear time-invariant stochastic system in the complex plane, we distinguish three kinds of stabilities: asymptotical mean square stability, critical stability and essential instability. While dealing with the criteria for essential instability, two methods are involved: the Lyapunov equation approach and the spectral analysis technique, which are the most common ways to characterize system stability.