Filtering for Discrete Fuzzy Stochastic Time-Delay Systems with Sensor Saturation

This paper addresses the <svg style="vertical-align:-3.3907pt;width:29.8375px;" id="M1" height="16.025" version="1.1" viewBox="0 0 29.8375 16.025" width="29.8375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,11.737)"><path id="x210B" d="M702 678l12 -14l-18 -14q-124 -96 -232 -310q25 10 62 21l53 18l33 43q101 126 187 195q88 70 135 70q57 0 57 -50q0 -78 -98 -145q-86 -58 -206 -105q-174 -251 -174 -334q0 -15 9.5 -25t24.5 -10q55 0 167 129l21 -13q-120 -146 -202 -146q-39 0 -63 24t-24 65&#xA;q0 101 104 262l-107 -41q-56 -110 -132 -193q-75 -82 -145 -109q-31 -11 -56 -11t-41 16.5t-16 43.5q0 129 283 247q17 29 20 33l22 36q1 2 9 13.5l14 20.5q18 28 59 77q34 39 87 86q-5 -1 -20 -1q-44 0 -124 44q-62 34 -102 34q-48 0 -82 -31q-34 -30 -34 -70q0 -44 22 -69&#xA;t66 -25q37 0 65 20.5t56 65.5l18 -9q-54 -107 -141 -107q-59 0 -93 34.5t-34 91.5q0 58 50 105q49 46 125 46q28 0 58 -11q35 -13 84 -38q59 -31 86 -31q42 0 80 19q16 9 42 28zM958 635q0 22 -24 22q-28 0 -86 -63q-56 -60 -128 -160q238 105 238 201zM307 241&#xA;q-110 -50 -165.5 -98t-55.5 -99q0 -24 24 -29q67 0 197 226z" /></g> <g transform="matrix(.012,-0,0,-.012,17.012,15.825)"><path id="x221E" d="M983 225q0 -112 -67 -174.5t-150 -62.5q-91 0 -154.5 43.5t-113.5 129.5q-49 -85 -104 -129t-138 -44q-98 0 -158.5 66t-60.5 154q0 59 21 106.5t54.5 75.5t70.5 43t73 15q90 0 152.5 -43.5t112.5 -128.5q48 84 104.5 128t140.5 44q93 0 155 -65t62 -158zM478 196&#xA;q-27 49 -47 80t-50 67t-64 54t-73 18q-48 0 -81.5 -47t-33.5 -128q0 -96 37.5 -157.5t99.5 -61.5q68 0 117.5 47t94.5 128zM889 204q0 91 -35.5 151t-99.5 60q-68 0 -119 -47t-95 -127q27 -49 47 -80.5t50 -67.5t65 -54t74 -18q113 0 113 183z" /></g> </svg> filtering problem for discrete fuzzy stochastic systems with time-varying delay and sensor saturation. Random noise depending on state and external disturbance is also taken into account. A decomposition approach is employed to solve the characteristic of sensor saturation. The scaled small gain (SSG) theorem is extended to the stochastic systems, which is employed to handle with the time-varying delay by transforming the original system into the form of an interconnected system consisting of two subsystems. By the proposed Lyapunov-Krasovskii function, the scaled small gains of the subsystems are analyzed, respectively. Sufficient conditions for the stochastic stability of the filtering error system with a prescribed <svg style="vertical-align:-3.3907pt;width:29.8375px;" id="M2" height="16.025" version="1.1" viewBox="0 0 29.8375 16.025" width="29.8375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,11.737)"><use xlink:href="#x210B"/></g> <g transform="matrix(.012,-0,0,-.012,17.012,15.825)"><use xlink:href="#x221E"/></g> </svg> level are established such that the gains of the <svg style="vertical-align:-3.3907pt;width:29.8375px;" id="M3" height="16.025" version="1.1" viewBox="0 0 29.8375 16.025" width="29.8375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,11.737)"><use xlink:href="#x210B"/></g> <g transform="matrix(.012,-0,0,-.012,17.012,15.825)"><use xlink:href="#x221E"/></g> </svg> filter can be obtained explicitly. Finally, simulation results are presented to demonstrate the effectiveness of the proposed approach.