Assume a linear discrete-time system is given by x(k+1)=[12?21?]x(k)+[01?]u(k)x(0)=x0?? Where x(k) is the state in time step k,u(k) is the control input and x(0) is the initial state. (a) What is the solution of the state x(k) ? (b) Analyze the stability of the system. (c) Analyze the controllability of the system.

Assume a linear discretetime system is given by x(k + 1) = [g i x(k) + ['1']u(k) x(0) = x0 Where x(k) is the state in time step k, u(k) is the control input and 1(0) is the initial state. (a) What is the solution of the state 150:)? (b) Analyze the stability of the system. (c) Analyze the controllability of the system