You can have one timer be the master and the others be the slaves.
Looking at the block diagram for timer 17 in reference manual (Figure 213), timer 17 cannot be a slave to any other timers.
I'll walk you through how to synchronize timer 1, 2 and 3 and if you can redo your timer assignments, you might be able to find a solution.
The TIMx_CR2 register's MMS field selects which event on a timer generates an event on that timer TRGO (or TRGO2 if it has one) signal.
The TIMx_SMCR register's TS field selects the trigger event source that timer will listen to.
The TIMx_SMCR register's SMS field select what that timer does when it gets the trigger / event.
Since we want timer 1 to be the master, configure its TRGO (in TIM1_CR2) to generate a TRGO when timer 1 is enabled (MMS[2:0] = 001
NOTE: The reference manual has an error on page 445 and it says: Bits 6:4 MMS[1:0]. Clearly it should say Bits 6:4 MMS[2:0]
Then, for timer 2 and 3, configure TIM2_SMCR and TIM3_SMCR, SMS[3:0] to 0110 to enable them when they receive an active edge on TRGI.
To select which signal to use for TRGI, we want timer 1 which using table 73 is ITR0 which means set TS[2:0] = 000
If for example, you could use timer 15 instead of timer 17, you will notice that it only has internal trigger connections to timer 2, 4, 16 OC1 and 17 OC2 (table 76). So, you cannot have timer 1 trigger timer 15!
What would could do is make timer 1, 3 and 15 slaves and timer 2 the master. Now, when you enable timer 2, the others will be simultaneously enabled.
