Mixed \(H_2/H_\infty\) robust output feedback control for uncertain linear systems (Q2705744)

The paper deals with the mixed \(H_2/H_\infty\) robust output feedback control problem for linear systems subjected to norm-bounded parameter uncertainty in both the state and the output matrices of the state space model. The class of systems under consideration is: NEWLINE\[NEWLINE\begin{aligned} \dot x(t) &= [A(t)+ \Delta A(t)] x(t)+ B_1u(t)+ B_2 w(t),\\ y(t) &= [C_1+ \Delta C_1(t)] x(t)+ D_1w(t),\\ z(t) &= C_2 x(t)+ D_2u(t),\end{aligned}NEWLINE\]NEWLINE where \(x(t)\in \mathbb{R}^n\) is the state, \(u(t)\in \mathbb{R}^n\) is the control input, \(w(t)\in \mathbb{R}^r\) is the disturbance, \(y(t)\in \mathbb{R}^n\) is the measurement, and \(z(t)\in \mathbb{R}^q\) is the controlled output, \(A\), \(B_1\), \(B_2\), \(C_1\), \(C_2\) and \(D_2\) describe the nominal system, \(\Delta A(t)\), \(\Delta C(t)\) are assumed to be of the form: NEWLINE\[NEWLINE\Delta A(t)= H_1F(t) E,\quad\Delta C_1(t)= H_2F(t)E,NEWLINE\]NEWLINE where \(F(t)\in \mathbb{R}^{i\times j}\) is an unknown matrix satisfying \(F^T(t) F(t)\leq I_i\), \(\forall t\).NEWLINENEWLINENEWLINEThe full order controllers derived are not only guaranteed to satisfy a prespecified \(H_\infty\) disturbance attenuation level for all admissible parameter uncertainties, but also provide an optimal bound for the worst-case \(H_2\) cost function.NEWLINENEWLINENEWLINEThe obtained results require the solutions of one parameter-dependent algebraic Riccati equation and three coupled parameter dependent nonlinear equations.NEWLINENEWLINENEWLINEA numerical algorithm for solving these parameter dependent nonlinear equations is also presented.