Hi there! I hope this isn't to vague, I'm rubbish at describing problems...

I have a nonlinear problem that I'm modelling in Matlab, and I want to maximise some of the states of the equation, while minimising others in response to a user input. To do this, I intend to linearise the equation about its equilibrium condition and write it in state space form, i.e.,

$\displaystyle \dot{x}(t)=A(t)x(t)+B(t)u(t)$

$\displaystyle y(t)=C(t)x(t)+D(t)u(t)$

$\displaystyle z(t)=E(t)x(t)+F(t)u(t)$

with my observed states y and z maximised and minimised respectively subject to a user input u. This means that I need to find an optimum user input u, and optimum controller matrix B(t) (with location and size constraints) for the system.

Does anyone know how to even begin solving this problem? I'm looking everywhere, but I don't know the key words to use to start looking for books. I've found loads of books titles 'optimal linear control' and such like, but nothing covering what I'm requiring.

Thanks in advance.