Discretized quasi‐time‐dependent ℋ∞ control for asynchronously switched systems with dynamic dwell‐time

Considering that actuator delay is inevitable and a discretized control design method is more preferable in practice, this article is concerned with the discretized quasi‐time‐dependent (QTD) ℋ∞ control for continuous‐time asynchronously switched systems via dynamic output‐feedback. The persistent dwell‐time (PDT) is employed to analyze the stability and ℒ2‐gain for switched systems in the framework of multiple QTD Lyapunov function approach, and the concept of dynamic dwell‐time (DDT) is used to characterize a category of switching signals for asynchronously switched systems with measurable switching lag, which means that the controlled plant can adjust its dwell‐time on some mode dynamically according to the switching lag of the corresponding controller. First, the stability and ℒ2‐gain are analyzed for switched systems with PDT. Then, by constructing controller‐dependent multiple QTD Lyapunov functions, a QTD control synthesis condition is derived based on the obtained stability criterion. The developed controller can guarantee the closed‐loop stability and ℋ∞ performance for the underlying system under a class of identified DDT switching signals. Subsequently, a discretized QTD control scheme is proposed by choosing the discretized quadratic version of the constructed Lyapunov functions. The synthesis condition is formulated as a set of finite‐dimensional LMIs, and hence it can be easily tractable. Finally, the proposed control scheme is applied to the tracking control of a mobile robot to illustrate its effectiveness and application potential.