Stability analysis and H_∞ control for uncertain stochastic piecewise-linear systems

The problem of the stochastic stability and H _infin control for uncertain stochastic piecewise-linear systems is studied. The stability analysis is based on Lyapunov functions that are continuous and piecewise quadratic. It is shown that the stability in the mean square for uncertain stochastic piecewise-linear systems can be established if a piecewise quadratic Lyapunov function can be constructed, and moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. It is also demonstrated via a numerical example that the stability result based on the piecewise quadratic Lyapunov functions is less conservative than that based on the common quadratic Lyapunov functions. The H _infin controllers can also be designed by solving a set of bilinear matrix inequalities (BMIs) based on the powerful piecewise quadratic Lyapunov function.