For the homogeneous dynamics of a linear system, suppose that the symmetric ma- trices P(t), Q(t) satisfy the Lyapunov equation, with P(t) bounded and uniformly positive definite, and Q(t) bounded. Let v(t) be the minimal eigenvalue of Q(t), i.e. v(t) = min \k(Q(t)) = k k Determine the "strongest property in order: inconslusive, stable, asymptotically stable, or exponentially stable) you can conclude for the following cases below. Show your reasoning carefully, and note that some or all of these cases might not fit neatly into the categories specifically considered in class. a.) v(t) = = -ce-t with c> 0. b.) v(t) = 1/t c.) v(t) = 1/2 = = For the homogeneous dynamics of a linear system, suppose that the symmetric ma- trices P(t), Q(t) satisfy the Lyapunov equation, with P(t) bounded and uniformly positive definite, and Q(t) bounded. Let v(t) be the minimal eigenvalue of Q(t), i.e. v(t) = min \k(Q(t)) = k k Determine the "strongest property in order: inconslusive, stable, asymptotically stable, or exponentially stable) you can conclude for the following cases below. Show your reasoning carefully, and note that some or all of these cases might not fit neatly into the categories specifically considered in class. a.) v(t) = = -ce-t with c> 0. b.) v(t) = 1/t c.) v(t) = 1/2 = =