Control of uncertain state-delay systems: Guaranteed cost approach (Q2711464)

This paper focuses on the problem of optimal guaranteed cost control based on the state feedback for the uncertain free delayed system NEWLINE\[NEWLINEx'(t)= [A+\Delta A(t)]x(t)+ [A_d+\Delta A_d(t)] x(t- \tau),\quad t\geq 0,NEWLINE\]NEWLINE and the problem of robust stability for the uncertain delayed system NEWLINE\[NEWLINEx'(t)= [A+\Delta A(t)] x(t)+ [B+\Delta B(t)] u(t)+ [A_d+\Delta A_d(t)] x(t-\tau),\quad t\geq 0.NEWLINE\]NEWLINE The author considers delay-independent and delay-dependent stabilities. Necessary and sufficient conditions are given in terms of algebraic Riccati inequalities and linear matrix inequalities.