Consider the linear time-invariant state-space model given by ₁ (t) = ax₁ (t) + 4x2(t) + 2u(t) *₂(t) = ax₂(t) y(t) = x1(

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Consider The Linear Time Invariant State Space Model Given By T Ax T 4x2 T 2u T T Ax T Y T X1 1 (150.88 KiB) Viewed 34 times

Consider the linear time-invariant state-space model given by ₁ (t) = ax₁ (t) + 4x2(t) + 2u(t) *₂(t) = ax₂(t) y(t) = x1(t) + x2(t) + u(t) where a is a real parameter (a € R). a. Study the internal stability of the system, determining for what values of a E R the system is asymptotic stable, marginally stable, or unstable. b. Study the controllability of the system: for what values of a Є R is the system fully controllable? c. Study the observability of the system: for what values of a € R is the system fully observable? d. Obtain the transfer function G(s) of the system. For what values of a E R is the system BIBO stable?