Reduced complexity control design for symmetric LPV systems

We use symmetry to reduce the computational complexity of designing parameter-dependent controllers and Lyapunov functions. We propose three complementary methods for exploiting symmetry to reduce the complexity. The first method uses symmetry to reduce the number of design variables. The second method uses symmetry to reduce the dimension of the design variables. And the third method reduces the number of linear matrix inequalities that the design variables must satisfy. We apply our reduced complexity control design to a building control problem. We show that, for this example, our method leads to an exponential decrease in the number of design variables and linear matrix inequalities.