Robust \(H_{\infty}\) continuous-discrete hybrid impulsive dynamic output feedback control for delays descriptor Markovian jump systems with multidimensional impulsive operator. (English) Zbl 1533.93172
Summary: This study focuses on the robust \(H_{\infty}\) continuous-discrete hybrid impulsive dynamic output feedback (DOF) control issue for time delays descriptor Markovian jump systems (TDDMJSs) with multidimensional impulsive operator. By applying an improved impulse-time-dependent Lyapunov-Krasovskii (L-K) functional, the novel \(H_{\infty}\) stochastic admissibilization conditions are formulated as linear matrix inequalities. A desired \(H_{\infty}\) hybrid impulsive DOF controller is achieved, which includes a continuous DOF controller and a discrete impulsive DOF controller. The \(H_{\infty}\) stochastic admissibilization of the closed-loop TDDMJSs can be satisfied by virtue of the desired hybrid impulsive DOF controller. In the end, the validity of the proposed \(H_{\infty}\) hybrid impulsive DOF controller design method is demonstrated by two examples, including an oil catalytic cracking process.
© 2023 John Wiley & Sons Ltd.
© 2023 John Wiley & Sons Ltd.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C27 | Impulsive control/observation systems |
| 93B52 | Feedback control |
| 93E03 | Stochastic systems in control theory (general) |
Keywords:
descriptor systems; dynamic output feedback control; Markovian jump systems; multidimensional impulsive operator; stochastic admissibilityReferences:
| [1] | XuS, LamJ. Robust Control and Filtering of Singular Systems. Springer‐Verlag; 2006. · Zbl 1114.93005 |
| [2] | ChangX, WangJ, ZhaoX. Peak‐to‐peak filtering for discrete‐time singular systems. IEEE Trans Circuits Syst Express Briefs. 2021;68(7):2543‐2547. |
| [3] | RahikainenJ, KianiM, SopanenJ, JalaliP, MikkolaA. Computationally efficient approach for simulation of multibody and hydraulic dynamics. Mech Mach Theory. 2018;130:435‐446. |
| [4] | QasemSN, MohammadzadehA. A deep learned type‐2 fuzzy neural network: singular value decomposition approach. Appl Soft Comput. 2021;105:107244. |
| [5] | DaiL. Singular Control Systems. Springer‐Verlag; 1989. · Zbl 0669.93034 |
| [6] | ChenW, JiangR, LuX, ZhengW. H_∞ control of linear singular time‐delay systems subject to impulsive perturbations. IET Control Theory Appl. 2017;11(3):420‐428. |
| [7] | WangY, ZhuangG, ChenF. Event‐based asynchronous dissipative filtering for T-S fuzzy singular Markovian jump systems with redundant channels. Nonlinear Anal Hybrid Syst. 2019;34:264‐283. · Zbl 1434.93099 |
| [8] | ChenW, ZhengW, LuX. Impulsive stabilization of a class of singular systems with time‐delays. Automatica. 2017;83:28‐36. · Zbl 1373.93268 |
| [9] | MuY, ZhangH, SunS, RenJ. Robust non‐fragile proportional plus derivative state feedback control for a class of uncertain Takagi‐Sugeno fuzzy singular systems. J Franklin Inst. 2019;356(12):6208‐6225. · Zbl 1416.93108 |
| [10] | HanY, KaoY, ParkJH. Robust nonfragile observer‐based control of switched discrete singular systems with time‐varying delays: a sliding mode control design. Int J Robust Nonlinear Control. 2019;29(5):1462‐1483. · Zbl 1410.93042 |
| [11] | ZhuangG, XiaJ, MaQ, SunW, WangY. Event‐triggered [( {H}_{\infty } \]\) feedback control for delayed singular jump systems based on sampled observer and exponential detector. Int J Robust Nonlinear Control. 2021;31(15):7298‐7316. · Zbl 1527.93309 |
| [12] | TangX, LiuZ. Sliding mode observer‐based adaptive control of uncertain singular systems with unknown time‐varying delay and nonlinear input. ISA Trans. 2022;128:133‐143. |
| [13] | ZhangW, ZhaoY, ShengL. Some remarks on stability of stochastic singular systems with state‐dependent noise. Automatica. 2015;51:273‐277. · Zbl 1309.93182 |
| [14] | LiX, SheK, ChengJ, ShiK, PengZ, ZhongS. Dissipativity‐based synthesis for semi‐Markovian systems with simultaneous probabilistic sensors and actuators faults: a modified event‐triggered strategy. ISA Trans. 2022;128:255‐275. |
| [15] | ZongG, QiW, KarimiHR. L_1 control of positive semi‐Markov jump systems with state delay. IEEE Trans Syst Man Cybern Syst. 2021;51(12):7569‐7578. |
| [16] | ChengP, HeS, LuanX, LiuF. Finite‐region asynchronous [( {H}_{\infty } \]\) control for 2D Markov jump systems. Automatica. 2021;129:109590. · Zbl 1478.93143 |
| [17] | SongJ, ZhouS, NiuY, CaoZ, HeS. Anti‐disturbance control for hidden Markovian jump systems: asynchronous disturbance observer approach. IEEE Trans Autom Control. 2023;68(11):6982‐6989. doi:10.1109/TAC.2023.3244153 · Zbl 07808199 |
| [18] | ZhuangG, XiaJ, SunW, FengJ, MaQ. Asynchronous admissibility and [( {H}_{\infty } \]\) fault detection for delayed implicit Markovian switching systems under hidden Markovian model mechanism. Int J Robust Nonlinear Control. 2021;31(15):7261‐7279. · Zbl 1527.93094 |
| [19] | KwonNK, ParkIS, ParkPG. H_∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities. Appl Math Comput. 2017;295:126‐135. · Zbl 1411.93170 |
| [20] | SongJ, NiuY, LamHK, ZouY. Asynchronous sliding mode control of singularly perturbed semi‐Markovian jump systems: application to an operational amplifier circuit. Automatica. 2020;118:109026. · Zbl 1447.93047 |
| [21] | YaoX, ParkJH, WuL, GuoL. Disturbance‐observer‐based composite hierarchical antidisturbance control for singular Markovian jump systems. IEEE Trans Autom Control. 2019;64(7):2875‐2882. · Zbl 1482.93642 |
| [22] | SongJ, WangZ, NiuY, DongH. Genetic‐algorithm‐assisted sliding‐mode control for networked state‐saturated systems over hidden Markov fading channels. IEEE Trans Cybern. 2021;51(7):3664‐3675. |
| [23] | ZhuangG, XiaJ, FengJ, SunW, ZhangB. Admissibilization for implicit jump systems with mixed retarded delays based on reciprocally convex integral inequality and Barbalat’s lemma. IEEE Trans Syst Man Cybern Syst. 2021;51(11):6808‐6818. |
| [24] | ZhangX, HanQ, GeX. Sufficient conditions for a class of matrix‐valued polynomial inequalities on closed intervals and application to [( {H}_{\infty } \]\) filtering for linear systems with time‐varying delays. Automatica. 2021;125:109390. · Zbl 1461.93515 |
| [25] | QianW, GaoY, YangY. Global consensus of multiagent systems with internal delays and communication delays. IEEE Trans Syst Man Cybern Syst. 2019;49(10):1961‐1970. |
| [26] | WuZ, SuH, ChuJ. H_∞ filtering for singular systems with time‐varying delay. Int J Robust Nonlinear Control. 2010;20(11):1269‐1284. · Zbl 1200.93133 |
| [27] | ZhangX, HanQ, GeX. Novel stability criteria for linear time‐delay systems using Lyapunov‐Krasovskii functionals with a cubic polynomial on time‐varying delay. IEEE/CAA J Automat Sin. 2021;8(1):77‐85. |
| [28] | WuZ, WuY, WuZG, LuJ. Event‐based synchronization of heterogeneous complex networks subject to transmission delays. IEEE Trans Syst Man Cybern Syst. 2018;48(12):2126‐2134. |
| [29] | LiY, WuY, HeS. Distributed consensus control for a group of autonomous marine vehicles with nonlinearity and external disturbances. Neurocomputing. 2021;443:380‐387. |
| [30] | WuY, GuangY, HeS, XinM. An industrial‐based framework for distributed control of heterogeneous network systems. IEEE Trans Syst Man Cybern Syst. 2020;50(6):2120‐2128. |
| [31] | LiX, LiP. Stability of time‐delay systems with impulsive control involving stabilizing delays. Automatica. 2021;124:109336. · Zbl 1461.93436 |
| [32] | ZhuangG, SunW, SuSF, XiaJ. Asynchronous feedback control for delayed fuzzy degenerate jump systems under observer‐based event‐driven characteristic. IEEE Trans Fuzzy Syst. 2021;29(12):3754‐3768. |
| [33] | FeiZ, GuanC, ZhaoX. Event‐triggered dynamic output feedback control for switched systems with frequent asynchronism. IEEE Trans Autom Control. 2020;65(7):3120‐3127. · Zbl 1533.93455 |
| [34] | YangD, LiX, QiuJ. Output tracking control of delayed switched systems via state‐dependent switching and dynamic output feedback. Nonlinear Anal Hybrid Syst. 2019;32:294‐305. · Zbl 1425.93149 |
| [35] | KwonNK, ParkIS, ParkPG, ParkCE. Dynamic output‐feedback control for singular Markovian jump system: LMI approach. IEEE Trans Autom Control. 2017;62(10):5396‐5400. · Zbl 1390.93836 |
| [36] | ParkCE, KwonNK, ParkPG. Dynamic output‐feedback [( {H}_{\infty } \]\) control for continuous‐time singular Markovian jump systems. Int J Robust Nonlinear Control. 2018;28(11):3521‐3531. · Zbl 1398.93101 |
| [37] | SunM, ZhuangG, XiaJ, MaQ, ChenG. Robust dynamic output feedback stabilization for uncertain singular Markovian jump systems with time‐varying delays. Int J Robust Nonlinear Control. 2022;32(6):3890‐3908. · Zbl 1527.93348 |
| [38] | YangT. Impulsive Control Theory. Springer Science & Business Media; 2001. · Zbl 0996.93003 |
| [39] | YangT. Impulsive control. IEEE Trans Autom Control. 1999;44(5):1081‐1083. · Zbl 0954.49022 |
| [40] | YaoJ, GuanZ, Ho DWCCG. Stability, robust stabilization and [( {H}_{\infty } \]\) control of singular‐impulsive systems via switching control. Syst Control Lett. 2006;55(11):879‐886. · Zbl 1113.93096 |
| [41] | TianK, GrebogiC, RenHP. Chaos generation with impulse control: application to non‐chaotic systems and circuit design. IEEE Trans Circuits Syst Regul Pap. 2021;68(7):3012‐3022. |
| [42] | LiX, PengD, CaoJ. Lyapunov stability for impulsive systems via event‐triggered impulsive control. IEEE Trans Autom Control. 2020;65(11):4908‐4913. · Zbl 1536.93638 |
| [43] | YanJ, ZhangD, HuB, GuanZ, ChenG, ChengX. Controllability analysis for a class of piecewise nonlinear impulsive non‐autonomous systems. Int J Robust Nonlinear Control. 2022;32(2):567‐582. · Zbl 1527.93023 |
| [44] | ZhanT, MaS, LiuX. Synchronization of singular switched complex networks via impulsive control with all nonsynchronized subnetworks. Int J Robust Nonlinear Control. 2019;29(14):4872‐4887. · Zbl 1426.93308 |
| [45] | WuH, LiC, WangY, HeZ, DengH. Stabilization of nonlinear dynamical systems via intermittent control with non‐instantaneous impulses and actuator saturation. ISA Trans. 2022;130:316‐324. |
| [46] | LiuY, ZhuangG, XieX, XiaJ. H_∞ asynchronous admissibilization for nonlinear singular delayed hybrid hydraulic turbine governing systems with impulsive perturbations. IEEE Trans Fuzzy Syst. 2023. doi:10.1109/TFUZZ.2023.3279294 |
| [47] | ZhuQ, ZhuangG, XiaJ, ChenG, FengJ. Robust [( {H}_{\infty } \]\) impulsive control for time‐varying delays descriptor jump systems based on impulse instants correlative L-K functional. Nonlinear Dyn. 2023;111(5):4737‐4751. |
| [48] | HolickiT, SchererCW. Output‐feedback synthesis for a class of aperiodic impulsive systems. IFAC‐PapersOnLine. 2020;53(2):7299‐7304. |
| [49] | ShiS, ZhangQ, YuanZ, LiuW. Hybrid impulsive control for switched singular systems. IET Control Theory Appl. 2011;5(1):103‐111. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
