I want to know if a second solution exists for the following math equation:
[math]Ce^{At} ρ_p+(CA)^{−1} (e^{At}−I)B=0[/math]Where C, ρ_p, A, and B are constant matrices, 't' is a scalar variable. I know that at least one solution i.e. t=θ_1 exists, but I want a method to determine if there is another [imath]θ_0 <θ_1[/imath] that is also a (second) solution. Any analytical way of determining that is what I am looking for.
[math]Ce^{At} ρ_p+(CA)^{−1} (e^{At}−I)B=0[/math]Where C, ρ_p, A, and B are constant matrices, 't' is a scalar variable. I know that at least one solution i.e. t=θ_1 exists, but I want a method to determine if there is another [imath]θ_0 <θ_1[/imath] that is also a (second) solution. Any analytical way of determining that is what I am looking for.
