Optimal guaranteed cost control of uncertain systems via static and dynamic output feedback
The authors consider the equation \(\dot x= [A+ D\Delta(t) E_1] x+ [B+ D\Delta(t) E_2] u\), \(x(0)= x_0\), with time-varying uncertain parameter-matrix \(\Delta (t)\) satisfying \(\Delta^\vdash(t)\Delta(t)\leq I\), and random initial condition \(x_0\) with covariance matrix \(\mathbb{E}(x_0 x_0')= I\); further, the read-out map \(y(t)= Cx(t)\) and a quadratic cost function \(j\) are considered. In order to make for the control \(u(t)= Ky(t)\) the closed-loop system quadratically stable and to minimize the cost function \(j\), a necessary condition is established in terms of the solution of a system of three parameter-dependent differential equations consisting of an equation for the gain \(k\), a Riccati and a Lyapunov equation.
scientific article; zbMATH DE number 885866
scientific article