This article addresses the problem of dissipative filtering for the delayed positive Roesser system with uncertainties under the try-once-discard communication protocol. To estimate the output of the addressed two-dimensional system, both positive lower- and upper-bounding filters are constructed, where the signals from the sensor nodes to the remote filters are transmitted through a shared communication network. To avoid the undesired data congestion phenomenon, the try-once-discard protocol is implemented to dynamically schedule the transmission sequence of the sensor nodes. Then, sufficient conditions are derived to design appropriate filters ensuring that the filtering error systems are positive, two-dimensional -γ-dissipative, and asymptotically stable. Finally, one numerical example is presented to demonstrate effectiveness of the designed filters.
GivoneDDRoesserRP. Multidimensional linear iterative circuits —general properties. IEEE Trans Comput1972; C-21(10): 1067–1073.
2.
RoesserRP. A discrete state-space model for linear image processing. IEEE Trans Autom Control1975; AC-20(1): 1–10.
3.
FornasiniE. A 2-D systems approach to river pollution modelling. Multidimens Syst Signal Process1991; 2(3): 233–265.
4.
KaczorekT. Two-dimensional linear systems. Berlin: Springer, 1985.
5.
BachelierOYeganefarNMehdiD, et al. On stabilization of 2D Roesser models. IEEE Trans Autom Control2017; 62(5): 2505–2511.
6.
YeganefarNYeganefarNGhamguiM, et al. Lyapunov theory for 2-D nonlinear Roesser models: application to asymptotic and exponential stability. IEEE Trans Autom Control2013; 5(8): 1299–1304.
7.
LiangJWangZHayatT, et al. Distributed state estimation for stochastic delayed 2-D systems with randomly varying nonlinearities over saturated sensor networks. Inf Sci2016; 370–371: 708–724.
8.
KhanaferABaşarTGharesifardB. Stability of epidemic models over directed graphs: a positive systems approach. Automatica2016; 74: 126–134.
9.
ZhuSHanQ-LZhangC. -gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: a linear programming approach. Automatica2014; 50(8): 2098–2107.
10.
HaddadWMHayakawaTBaileyJM. Adaptive control for nonlinear compartmental dynamical systems with applications to clinical pharmacology. Syst Control Lett2006; 55(1): 62–70.
KnornFMasonOShortenR. On linear co-positive Lyapunov functions for sets of linear positive systems. Automatica2009; 45(8): 1943–1947.
13.
HongMTHienLVMinh-HangTT. Static output-feedback peak-to-peak gain control of discrete-time positive linear systems with diverse interval delays. Proc Inst Mech Eng Part I J Syst Control Eng2022; 236(8): 1578–1589.
14.
ChenJYangYDuB. Non-overshoot tracking control for positive continuous-time linear systems. Proc Inst Mech Eng Part I J Syst Control Eng2023; 237(1): 35–42.
15.
LiuXYuWWangL. Necessary and sufficient asymptotic stability criterion for 2-D positive systems with time-varying state delays described by Roesser model. IET Contr Theory Appl2011; 5(5): 663–668.
16.
WangJLiangJWangL. Switched mechanisms for stability and -gain analysis of T-S fuzzy positive systems described by the F-M second model. J Frankl Inst2018; 355(3): 1351–1372.
17.
HienLVTrinhHMPathiranaPN. On -gain control of 2-D positive Roesser systems with directional delays: necessary and sufficient conditions. Automatica2020; 112: 108720.
18.
DuanZHanYXiangZ, et al. On -gain control for 2D delayed positive systems in FM LSS models: necessary and sufficient conditions. Int J Syst Sci2022; 53(16): 3449–3464.
19.
DuanZAhnCKXiangZ, et al. -gain controller design for 2-D Markov jump positive systems with directional delays. IEEE Trans Syst Man Cybern Syst2022; 52(12): 7600–7613.
20.
ZhangNLiangJLiD. PID output-feedback control and filtering for positive Roesser system. Circuits Syst Signal Process. Epub ahead of print 21 August 2023. DOI: 10.1007/s00034-023-02484-2
21.
ZhangWBranickyMSPhillipsSM. Stability of networked control systems. IEEE Control Syst Mag2001; 21(1): 84–99.
22.
WuJZhongJLiuY, et al. State estimation of networked finite state machine with communication delays and losses. IEEE Trans Circuits Syst II-Express Briefs2022; 69(3): 1372–1376.
23.
ZouLWangZHanQ-L, et al. Ultimate boundedness control for networked systems with try-once-discard protocol and uniform quantization effects. IEEE Trans Autom Control2017; 62(12): 6582–6588.
24.
ZouLWangZHuJ, et al. Communication-protocol-based analysis and synthesis of networked systems: progress, prospects and challenges. Int J Syst Sci2021; 52(14): 3013–3034.
25.
SuYCaiHHuangJ. The cooperative output regulation by the distributed observer approach. Int J Netw Dyn Intell2022; 1(1): 20–35.
26.
ZhuCZhangPLuZ, et al. Recursive filtering for time-varying systems with mixed time-delays subject to stochastic communication protocol and dynamic quantization effects. Proc Inst Mech Eng Part I J Syst Control Eng. Epub ahead of print 5 July 2023. DOI: 10.1177/09596518231179887
27.
XueMTangYRenW, et al. Stability of multi-dimensional switched systems with an application to open multi-agent systems. Automatica2022; 146: 110644.
28.
FangJLiuWChenL, et al. A survey of algorithms, applications and trends for particle swarm optimization. Int J Netw Dyn Intell2023; 2(1): 24–50.
29.
WangFWangZLiangJ, et al. Resilient filtering for linear time-varying repetitive processes under uniform quantizations and Round-Robin protocols. IEEE Trans Circuits Syst I Regul Pap2018; 65(9): 2992–3004.
30.
LiDLiangJWangF. Robust filtering for 2D systems with RON under the stochastic communication protocol. IET Contr Theory Appl2020; 14(18): 2795–2804.
31.
WangJLiangJYangJ. Nonfragile dynamic output-feedback control for positive singular systems under the switched mechanism and Round-Robin protocol. Nonlinear Anal-Hybrid Syst2023; 47: 101292.
WillemsJC. Dissipative dynamical systems–part II: linear systems with quadratic supply rates. Arch Ration Mech Anal1972; 45: 352–393.
34.
HillDJMoylanPJ. Connections between finite-gain and asymptotic stability. IEEE Trans Autom Control1980; AC-25(5): 931–936.
35.
LiangSLiangJQiuJ. Finite-time input-to-state stability of discrete-time stochastic switched systems: a comparison principle-based method. Int J Syst Sci2023; 54(1): 1–16.
36.
KchaouMRegaiegMA. Event-triggered extended dissipativity fuzzy filter design for nonlinear Markovian switching systems against deception attacks. Mathematics2023; 11(9): 2064.
37.
ZhaoYWuBZhangW. Finite-time exponentially extended dissipative filtering for singular time-delay Markov jump systems with quantized outputs based on hidden Markov mode. Int J Robust Nonlinear Control2023; 33(11): 6431–6458.
38.
HaddadWMChellaboinaVRajpurohitT. Dissipativity theory for nonnegative and compartmental dynamical systems with time delay. IEEE Trans Autom Control2004; 49(5): 747–751.
39.
AhnCKShiPBasinMV. Two-dimensional dissipative control and filtering for Roesser model. IEEE Trans Autom Control2015; 60(7): 1745–1759.
40.
LiDLiangJWangF. Dissipative networked filtering for two-dimensional systems with randomly occurring uncertainties and redundant channels. Neurocomputing2019; 369: 1–10.
41.
YangRLiLShiP. Dissipativity-based two-dimensional control and filtering for a class of switched systems. IEEE Trans Syst Man Cybern Syst2021; 51(5): 2737–2750.
42.
WangJLiangJZhangC-T. Dissipativity analysis and synthesis for positive Roesser systems under the switched mechanism and Takagi-Sugeno fuzzy rules. Inf Sci2021; 546: 234–252.
43.
WangJLiangJZhangC-T, et al. Robust dissipative filtering for impulsive switched positive systems described by the Fornasini-Marchesini second model. J Frankl Inst2022; 359(1): 123–144.
44.
KaczorekT. Positive 1D and 2D systems. London: Springer, 2002.
