Guaranteed Cost Sliding Mode Control of Switched Systems with Known Sojourn Probabilities

Zhao, Hongfei; Niu, Yugang

doi:10.1007/s12555-018-0093-y

Cited by 4 publications

(7 citation statements)

References 21 publications

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“…i , similar to the above analysis, inequality (37) in Theorem 2 and inequality (53) in Theorem 3 can be ensured by condition (71). Moreover, by Schur's complement, equalities (10)- (12) in Theorem 1 and condition (54) in Theorem 3 can be guaranteed by the LMIs (72)-(75).…”

Section: Design Of K I and Imentioning

confidence: 95%

“…Consider the closed-loop switched system (7) with w(k) ≠ 0. Suppose that, for given ui > 0, 0 < si < 1, 1i > 0, 2i > 0, and i > 0, there exist matrices P ij > 0, P ii > 0 and scalars 1i ,̄1 i , i , and j (∀ i, ∈ ), satisfying conditions (10)- (12) and the following inequalities:…”

Section: Theoremmentioning

confidence: 99%

“…Consider the switched system (2) with the specified sliding function (4) and the mode-dependent SMC law (5). Suppose that there exist matrices P ij > 0, P ii > 0, W ij > 0, W ii > 0 and scalars 1i ,̄1 i , 2i ,̄2 i , i , j satisfying conditions (10)- (12) and the following inequalities for any i, ∈ :…”

Section: The Reachabilitymentioning

confidence: 99%

“…However, if the dwell time of system mode i is enough long such that the MDADT condition (13) is satisfied, that is, the synchronous interval [k l + △ l , k l+1 ) is enough long in which the function V 2 (k) is monotonically decreasing, it can be obtained that V 2 (k l+1 ) < V 2 (k l ). Actually, during the whole interval k ∈ [k l , k l+1 ), by combining the above expressions (61) and (63) and conditions (12) and (54), we can get…”

Section: The Reachabilitymentioning

confidence: 99%

“…Owing to the significance both in practical applications and theoretical research, switched systems have been widely investigated in many fields, such as robotics, power electronics, chemical processes, aircraft and air traffic control, etc, and lots of exciting results have been obtained on the stability and stabilization problems for switched systems in the past decade . Especially, sliding mode control (SMC) method, as an effective robust control technique, has been also successfully applied in uncertain switched systems, stochastic systems, and other systems . For example, the SMC problem was considered in the work of Wu and Lam for uncertain switched systems with the same control input matrices for all subsystems.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Sliding mode control of discrete‐time switched systems subject to mode delays

Zhao

Niu

2019

Intl J Robust & Nonlinear

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Summary This work considers the sliding mode control problem of a class of discrete‐time uncertain switched systems subject to detecting‐delay on mode signals, which may result in the asynchronous phenomenon between the controller and the switched system. Since the mode information of the controlled system is not available for the controller in time, a mode‐independent sliding surface will be introduced, by which an asynchronous sliding mode controller is designed, whose control gain and robust parameter will be changing according to the controller mode. In the analysis on the stability of the closed‐loop control system and the reachability of the specified sliding surface, the asynchronous characteristics are detailedly investigated. It is shown that the Lyapunov function may be not always decreasing along the state trajectories during the unmatched interval of controller modes and system modes. Nevertheless, it is proven that the state trajectories can be driven into a sliding region around the specified sliding surface in finite time. Finally, some numerical simulation results are provided.

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Section: Design Of K I and Imentioning

confidence: 95%

Section: Theoremmentioning

confidence: 99%

Section: The Reachabilitymentioning

confidence: 99%

Section: The Reachabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sliding mode control of discrete‐time switched systems subject to mode delays

Zhao

Niu

2019

Intl J Robust & Nonlinear

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Protocol‐based collaborative design for discrete‐time switched systems with sojourn probabilities

Zhu

Wei

et al. 2020

Intl J Robust & Nonlinear

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This article focuses on the collaborative design of a class of discrete-time switched systems with sojourn probabilities. For the purpose of preventing the data collision, the Try-Once-Discard (TOD) protocol is employed to govern the information transmission between sensors and the controller. Moreover, it is worth noting that the values of sojourn probabilities, which are not given ahead, have an effect on the system stability. As a consequence, a novel collaborative design framework is established, in which the sojourn probability and static output-feedback controller are to be designed simultaneously. By considering the effect from the TOD protocol and using the Lyapunov function related to the mode and protocol, a sufficient condition is derived to guarantee the exponential mean square stability of the closed-loop system with a prescribed lower bound on the decay rate. Then, the desired sojourn probabilities and controller gains dependent on the corresponding mode and protocol are obtained in terms of convex optimization method with equality constraints. Subsequently, an estimation approach is provided to estimate the decay rate and decay coefficient of the closed-loop system. Finally, one numerical example is given to testify the effectiveness of the proposed design approach.

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