Example 3.5 Determine the equilibrium points of thefollowing systemxi = -X2X2 = -Xi - X2Solution The system is a LTI system. By lettingX = [xix, J , the system can be described by.0X = AX =X-1 Obviously, the system matrix A is nonsingular. By lettingX = 0, it can be deduced that the origin X。 = 0 of the statespace is the only equilibrium point of the system
Example 3.6 Determine the equilibrium points of thefollowing systemX = -XiX2 = Xi + X2 -x3SolutionObviously, the system is a non-linear systemg X=[x x,] and letting X=o ， threeBy lettingequilibrium points of the system can be obtained as[o][o]0X.XX001