H_∽performance controller parameterisation of linear switching plants under uncontrolled switching

Weighted L 2 gain performance controller parameterisation of linear switching plants with average dwell time

“…The coupled Riccati inequalities‐based controller parameterisation problem given in Theorem 1 is transferred equivalently to LMI‐based optimisation problem in Theorem 3. The determination of the minimal weighted gain with respect to given and can be formulated and solved as an LMI optimisation problem: Remark 4 In particular, just as introduced in [35], when switching is uncontrolled, namely governed by some arbitrary switching rule, a common Lyapunov function is usually used to guarantee the stability or control performance, i.e. and .…”

“…As is known, the regular problem can be solved by the famous Riccati equation‐based algorithm [34], which has also provided a parameterisation of all possible stabilising controllers guaranteeing a bound of performance of the closed‐loop system. Based on Riccati inequalities, the controller parameterisation of linear switching plants was presented under uncontrolled switching in [35]. Since only one constant Lyapunov function is adopted for the controller parameterisation, compared with the MLFs‐based method, the result is relatively conservative [36, 37].…”