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Summary: In this paper, we study the absolute stability and H∞$$ {H}_{\infty } $$ control problem for switched Lurie system (SLS) under asynchronous switching. A novel Lyapunov‐Lurie function is constructed, which is discontinuous and allowed to increase at the switching instants and the instants when controller modes and system modes are matched. Considering the superiority of time‐varying Lyapunov function technique, this paper is concerned with the Lyapunov‐Lurie function with time‐varying characteristic. Then, based on the switched time‐varying Lyapunov‐Lurie function (STVLLF) and mode‐dependent minimum dwell time (MDMDT) method, some control synthesis conditions are derived. The developed controller can guarantee the absolute stability and L2$$ {L}_2 $$‐gain performance for the closed‐loop SLS with admissible switching lag. Subsequently, a time‐varying control scheme is proposed from the STVLLF. H∞$$ {H}_{\infty } $$ control synthesis conditions in terms of linear matrix inequalities are established, which improve the existing results. Finally, two numerical examples are considered to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

This article deals with the H ∞ control problems of switched Lurie systems. Our purpose is to design switching signals and state feedback controllers with time-varying control gains that make the closed-loop switched Lurie systems absolutely stable. Based on switched time-varying Lyapunov–Lurie function, time-varying controllers corresponding to two kinds of switching signals are proposed. On this basis, the control synthesis conditions are given. It is worth mentioning that our results can deal with the situation that all subsystems are not stabilizable. Finally, the obtained results are applied to a flexible joint robotic arm model with switchings of parameter values. Another simulation example of switched Lurie systems is considered to illustrate the validity of the presented approaches. [ABSTRACT FROM AUTHOR]

In this article, we study the absolute stabilization of switched Lurie system via dynamic output feedback, where the nonlinearity is unknown and is restricted in a sector. In most works, the nonlinearity is assumed to be known exactly or is restricted in a bounded sector. Here, we consider the most general case with unbounded sector. With the help of switched time‐varying Lyapunov–Lurie function, a dynamic output feedback controller with time‐varying control gain is presented. On this basis, sufficient conditions for absolute stabilization are derived in the framework of mode‐dependent minimum dwell time and mode‐dependent range dwell time. It turns out that this time‐varying control strategy can solve the absolute stabilization of switched Lurie systems that all subsystems are not stabilizable. Moreover, the stability criteria in terms of linear matrix inequality we derived can be easily checked via Matlab toolbox. Finally, the effectiveness of presented methods is verified by several numerical examples. [ABSTRACT FROM AUTHOR]

This article considers the asymptotic stability of switched positive linear time‐delay system with all subsystems unstable. By constructing new discretized co‐positive Lyapunov‐Krasovskii functions, stability conditions are derived for both the discrete time‐varying delay and distributed time‐varying delay cases. Then the results are also extended to nonpositive switched delay systems. Finally we apply our results to consensus problems of switched multi‐agent systems with time delay. We propose numerical examples to illustrate our approach. [ABSTRACT FROM AUTHOR]