This paper is concerned with exploring an extended approach for the stability analysis and synthesis for Markovian jump nonlinear systems (MJNLSs) via fuzzy control. The Takagi-Sugeno (T-S) fuzzy model is employed to represent the MJNLSs with incomplete transition description. In this paper, not all the elements of the rate transition matrices (RTMs), or probability transition matrices (PTMs) are assumed to be known. By fully considering the properties of the RTMs and PTMs, sufficient criteria of stability and stabilization is obtained in both continuous and discrete-time. Stabilization conditions with a mode-dependent fuzzy controller are derived for Markovian jump fuzzy systems in terms of linear matrix inequalities (LMIs), which can be readily solved by using existing LMI optimization techniques. Finally, illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.

In this paper, a stochastic asymptotic stabilization method is proposed for deterministic input-affine control systems, which are randomized by including Gaussian white noises in control inputs. The sufficient condition is derived for the diffusion coefficients so that there exist stochastic control Lyapunov functions for the systems. To illustrate the usefulness of the sufficient condition, the authors propose the stochastic continuous feedback law, which makes the origin of the Brockett integrator become globally asymptotically stable in probability.