2)State space descriptioncdu.( =i (t)(1.1)dtdir (t)(1.2)+ R.i,(t)+u(t) = u(t)dtx(t) =u.(t)儿Define statevariablesxz(t) =it(t)1x(t)x2(t)(1.6)R1x2(t) =u(t)x(t)(tLLL(1.7)几10x(t)xi(t)C(1.8)1[u(t)]R[x2 (t)x2(t)LLI
( ) 1 ( ) 1 2 x t C x t = ( ) 1 ( ) ( ) 1 ( ) 2 1 2 u t L x t L R x t L x t = − − + (1.6) (1.7) 2）State space description ( ) d d ( ) i t t u t C L c = ( ) ( ) ( ) d d ( ) R i t u t u t t i t L L c L + + = （1.1） （1.2） ( ) ( ) 1 x t u t = c ( ) ( ) 2 x t i t = L Define state variables 1 ( ) 0 ( ) ( ) 1 1 0 ( ) ( ) 2 1 2 1 u t L x t x t L R L C x t x t + − − = (1.8)
: (1.8) eoieecarX0- x() 0) X(t)=AX(t+bu(t) (1.9) 咖w8及 4()=u()] The set of differential equations in matrix form (1.8)or (1.9) is called the state equation(状态方程)of the system
1 ( ) 0 ( ) ( ) 1 1 0 ( ) ( ) 2 1 2 1 u t L x t x t L R L C x t x t + − − = (1.8) X(t) = AX(t) + bu(t) (1.9) where = ( ) ( ) ( ) 2 1 x t x t t X − − = L R L C 1 1 0 A = L 1 0 b u(t) = u(t) The set of differential equations in matrix form (1.8) or（1.9） is called the state equation（状态方程） of the system. Define state vector 1 2 ( ) ( ) ( ) x t X t x t =