Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers (Q5960319)

The following uncertain control systems are studied NEWLINE\[NEWLINE \dot{x}(t)=(A_{0}+D_{0}F_{0}(t)E_{0})x(t)+\int_{-r}^{0}(A(\Theta)+D(\Theta) F(t,\Theta)E(\Theta))x(t+\Theta)d\Theta+Bu(t), NEWLINE\]NEWLINE where \(F_{0}(t)\) and \(F(t,\Theta)\) are unknown matrix-valued functions satisfying the conditions NEWLINE\[NEWLINE \parallel F_{0}(t)\parallel\leq 1, \parallel F(t,\Theta)\parallel\leq 1, t\in[0,\infty), \Theta\in[-r,0]. NEWLINE\]NEWLINE NEWLINENEWLINENEWLINESufficient conditions for robust stability \((u(t)\equiv 0)\) and robust stabilization \((u(t)=kx(t))\) of the equilibrium solution \(x(t)\equiv 0\) are obtained in the form of an LMI. As an application, the stabilization problem of combustion in the chamber of a rocket motor is investigated.