@Preben Alsholm 

without stopping the computation is possible to continue calculating ? that the value function V is not changed after the trigger ? For example, if the trigger fires in the first second , and we must continue to calculate the tenth of a second . Another example . At the input of the integrator receives the function V , which is a linearly increasing function from zero to infinity . Integrator output is variable X . As soon as the function V will be equal to one, a further increase in the value function V is terminated. Thus the input of the integrator constant. But the value of the integrator output should continue to be evaluated 

@Preben Alsholm 

I tried to replicate your program, but Maple generated an error. Could you give the program completely?

@Preben Alsholm 

Time t = 0 .. infinity or t = 0 .. constant. The time t can not be less than 0. Value function U should be limited. A maximum of the function U (t) can be one 1(t) and the minimum of the function U(t) can be 0 (t) at any point in time is not negative. How to limit the value of the function at the findability within the function dsolve.

For example Simulink have block called "limit". If you make a differential equation in Simulink, the feedback you can put a limit on the value of U. I want to get the same in Maple.