Improved bounded real lemma for continuous-time stochastic systems with polytopic uncertainties

By decoupling product terms between the Lyapunov matrix and system matrices, this paper proposes a parameter-dependent bounded real lemma (BRL) for continuous-time stochastic systems with polytopic uncertainties. This new criterion is shown, via a numerical example, to be much less conservative than previous result in the quadratic framework. In addition, the obtained result is further extended to cope with stochastic systems with time-varying state delay. All of the improved BRL are expressed as strict linear matrix inequality (LMI) conditions, which can be easily tested by using standard numerical software.