make the definitions, x,(t)=u,(t) and x,(t) =i,(t)RLYYY100x(t)cx (t)一11.u.(t)1R[x (t)x(t)LLLstateequationy(t) = u.(t)It can be expressed in matrix form notation asx()y(t)=[1 0output equationx(t)
100>x(t)x (t)c1[u(t)]state equation十1R[x (0)x,(t)LZLx(t)output equation0y(t) =[1x(t)x(t)x(t)X(t) =X(t) =x, (t)x,(t)It can also be expressed in a more compact form asX(t) = AX(t) + bu(t)state equationstate space modeloutput equationy(t) = cX(t) + du(t)The state space model is an internal model of system
1.1.2 Several DefinitionsDefinition 1.1 The state of a system is a minimum set ofvariables x,, called state variables, to describe the system'sbehavior.(1) The components of state, which are those state variablesare linearly independent at any instant, in other words, x,cannot be expressed linearlyby x,, j+ i,i, j =l,2,..,n
1.1.2 Several Definitions
1.1.2 Several DefinitionsDefinition 1.1 The state of a system is a minimum set ofvariables x,, called state variables, to describe the system'sbehavior. +(2) The initial values of this set and the inputs of system forte (to,co) are sufficient to describe uniquely the system'sresponse for all t≥t.. The state at any fixed time can berepresented by the values of a set of state variablesx,,i = 1,2, .., n
1.1.2 Several Definitions