You want the singular points.
For your
expr := (a-b) / (b-a^3);    # be careful with the parentheses!
singular( expr, {a,b} );
      {a = a, b = a^3}

So, you have infinitely many singular points (a is arbitrary and b=a^3).

It is not clear what are your intentions. For a minimization problem, usually the command detects the singularities.
E.g.

minimize(1/x, x=-1..2, location);
    -infinity, {[{x = 0}, -infinity]}

You cannot. And you do not need this.
CompressedSparseForm  is supposed to be used for external programs/platforms.

L must be numeric.

restart;
with(IntegrationTools):
L:=5:
simplify(int(f(x), x = 0 .. L*Ts)-Split(int(f(x), x = 0 .. L*Ts), [i*Ts, i = 0 .. L])):lprint(%);
       int(f(x), x = 0 .. 5*Ts)-(int(f(x), x = 0 .. Ts)) -
         (int(f(x), x = Ts .. 2*Ts))-(int(f(x), x = 2*Ts .. 3*Ts))-(int(f(x), x = 3*Ts .. 4*Ts))-(int(f(x), x = 4*Ts .. 5*Ts))
combine(%);

         0

If you just want to parallelize some numerical computations (without int, sum etc, see ?thread-safe) you can use Threads:-Seq.
Example

f := proc(i) local k; 
if   i=1 then    add(1/evalf((k+sin(k))^(k/(k+1))),k=1..5*10^4)
elif i=2 then    add(1/evalf((k+sin(k))^(k/(k+2))),k=1..6*10^4)
elif i=3 then    add(1/evalf((k+sin(k))^(k/(k+3))),k=1..6*10^4)
elif i=4 then    add(1/evalf((k+sin(k))^(k/(k+4))),k=1..3*10^4)
fi
end:

CodeTools:-Usage([Threads:-Seq(f(i), i=1..4)]);
CodeTools:-Usage([seq(f(i), i=1..4)]);  # without threads, for comparison

P:=proc(n::nonnegint,k::nonnegint) 
if n<1 or k<1 or k>n then return NULL fi;
if k=1 then return [n] fi;
if k=n then return [1$n] fi;
seq([u[]+~1], u=[P(n-k,k)]), seq([1,u[]], u=[P(n-1,k-1)])
end: 

CodeTools:-Usage(nops([P(100, 5)]));
memory used=323.13MiB, alloc change=76.01MiB, cpu time=2.07s, real time=1.94s, gc time=374.40ms
                             38225

CodeTools:-Usage(nops([P(80, 10)]));
memory used=3.28GiB, alloc change=435.74MiB, cpu time=29.73s, real time=23.37s, gc time=9.70s
                             533975

sort~(MM);          

1. The exponential of a vector v does not exist in maths. If you want to apply exp elementwise then use exp~(v)  or map(exp, v)
==>  < exp(v[1]), exp(v[2]), ... > .  Note that for a square matrix M there is MatrixExponential(M).

2. To integrate a matrix M (elementwise also)  use  map(int, M, t=a..b)  or map(int, M, [x=a..b, y=c..d,...] ).

3. You cannot have in an integral both  vx  and  vx(x,t)  and integrate wrt  vx.

LinearMultivariateSystem has a bug.
Use solve or SolveTools:-SemiAlgebraic  instead.

P.S. If you really need LinearMultivariateSystem  then:

sys1:=subsindets(sys, indexed, e -> cat(op(0,e),__, op(e)));
SolveTools:-Inequality:-LinearMultivariateSystem(sys1,indets(sys1));

This form of eval is an "intelligent" subs. In the second example, a subs was possible. In the first one, subs would produce a nonsense, so the expression was left practically untouched (you can check this using lprint). It is the typesetting system which produced the ...|{x=0} display.

NonegComb:=proc(M::Matrix,v::Vector)
local n:=upperbound(M,2), L, t, S;
if upperbound(M,1) <> upperbound(v) then error "Incompatible vector" fi;
L:=convert(add(M[..,i]*t[i],i=1..n)-v,list);
S:=simplex:-minimize(0, [(L=~0)[],  seq(t[i]>=0, i=1..n)]);
if S={} then return false fi;
eval([seq(t[i],i=1..n)],  S);
end:

M:=Matrix([[3, 0, 2, 2, 1, 1], [-1, -1, 0, -1, 0, -1], [0, 3, 0, 1, 1, 2], [3, 0, 1, 2, 0, 1], [-1, -1, -1, -1, -1, -1]]):
v1:= Vector[column](5, [3, 1, 0, 0, -2]):
v2 := M[..,1]+7*M[..,2]+9*M[..,4]:
NonegComb(M,v1);
                             false
NonegComb(M,v2);
                     [0, 13/2, 0, 21/2, 0, 0]

P:=n->seq(seq([a,b,n-a-b],b=max(a, floor(n/2)-a+1)..floor((n-a)/2)), a=1..floor(n/3)):

P(36); nops([%]);
[2,17,17],[3,16,17],[4,15,17],[4,16,16],[5,14,17],[5,15,16],[6,13,17],[6,14,16],[6,15,15],[7,12,17],[7,13,16],[7,14,15],[8,11,17],[8,12,16],[8,13,15],[8,14,14],[9,10,17],[9,11,16],[9,12,15],[9,13,14],[10,10,16],[10,11,15],[10,12,14],[10,13,13],[11,11,14],[11,12,13],[12,12,12]
      27

I have also tried SolveTools:-SemiAlgebraic  and I had to interrupt it.
Probably the decomposition is very large.
The problem can be managed with PolyhedralSets.

restart;
ineqs:= [-a1-a2+a3+a4 <= 2, a1+a2 <= 3, -2*a1 <= -1, -2*a2 <= -1, -2*a3 <= -1, -2*a4 <= -1, -a1+a2+a3-a4 <= 4, -a1+a2-a3+a4 <= 4, a1-a2+a3-a4 <= 4, a1-a2-a3+a4 <= 4]:
with(PolyhedralSets):
ps := PolyhedralSet(ineqs):
vertices:=VerticesAndRays(ps)[1];

vertices := [[1/2, 5/2, 1/2, 5/2], [1/2, 5/2, 3/2, 7/2], [3/2, 3/2, 1/2, 9/2], [1/2, 5/2, 5/2, 1/2], [1/2, 5/2, 7/2, 3/2], [3/2, 3/2, 9/2, 1/2], [1/2, 5/2, 1/2, 1/2], [5/2, 1/2, 3/2, 7/2], [5/2, 1/2, 1/2, 5/2], [5/2, 1/2, 1/2, 1/2], [5/2, 1/2, 7/2, 3/2], [5/2, 1/2, 5/2, 1/2], [1/2, 3/2, 1/2, 7/2], [1/2, 3/2, 7/2, 1/2], [1/2, 1/2, 5/2, 1/2], [1/2, 1/2, 1/2, 5/2], [1/2, 1/2, 1/2, 1/2], [3/2, 1/2, 1/2, 7/2], [3/2, 1/2, 7/2, 1/2]]

So, there are 19 vertices. The solution of your system can be expressed as a convex combination with 19 parameters
(actually 18 if  t1+...+t19=1  is used).
Conclusion: the problem is not as simple as it seems.

The problem is more general. E.g.    int(f(alpha),alpha=0..1) * L;   latex(%);
Workaround:

restart;
MyLI_:=eval(`latex/int`):
`latex/int` := proc() MyLI_(args)," " end: