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H∞ control scheme research of piecewise affine discrete-time systems based on describing regions as polyhedra

This paper researches the disturbance attenuation problem of discrete-time PWA (piecewise affine) systems. Firstly, An approach of H∞ control scheme, which describe the system regions as polyhedra, is presented. The basic idea is to construct piecewise quadratic Lyapunov function and introduce a dissipation inequality to guarantee the system energy dissipation. The designed controllers not only guarantee the stability of the closed-loop systems, but also obtain the disturbance attenuation ability. The results can be formulated as bilinear matrix inequalities. Then, the presented approach is compared with the current approach which describes the system regions as ellipsoids and formulates the results as linear matrix inequalities.