It is desirable to use well-designed controllers to maintain building temperature with solar collector space-heating systems. One solar heating system can be described by [10]

and dx (t) dt 3x1 (t) + u (t) + u (t), dx2(t) = 2x2(t)+u2(t)+d(t), where x(t) dt temperature deviation from desired equilibrium, and x2(t) = temperature of the storage material (such as a water tank). Also, u (t) and u (t) are the respective flow rates of conventional and solar heat, where the transport medium is forced air. A solar disturbance on the storage temperature (such as overcast skies) is represented by d(t). Write the ma- trix equations and solve for the system response when u(t)=0, u2(t)=1, and d(t) = 1, with zero initial conditions.