Robust H∞ control for constrained discrete-time piecewise affine systems with time-varying parametric uncertainties

In this study, a novel robust H _infin control scheme is presented for discrete-time piecewise affine (PWA) systems in the presence of time-varying uncertainties, external disturbance and time-domain constraints. The suggested control method is formulated as linear matrix inequalities (LMIs), and solved much more efficiently than current methods which could be only cast as bilinear matrix inequalities (BMIs). The key ideas are to introduce a parameter-dependent piecewise-quadratic Lyapunov function (PDPWQLF) to guarantee the closed-loop system to be energy dissipative, and use the concept of approximating polytopic operating regions by ellipsoids. The resulting controller can guarantee robust closed-loop properties, including stability, H _infin performance and the satisfaction of constraints. An example is presented to verify the proposed theoretical results.