If this Ceritinib assumption is not satisfied, a stabilizing output feedback controller is required.When the sensors in the NCSs experience faults, we consider the following sensor stuck fault model similar to [28],yFi(k)=Fiy(k)+(I?Fi)ysi(k),i=0,1,2,��,q(2)where q is the quantity of the possible Inhibitors,Modulators,Libraries fault modes andysi(k)=[ysi1(k)ysi2(k)��ysim(k)]T(3)with ysij(k)(j = 1, 2,��, m) being the low frequency fault of the kth sensor. Further, Fi is defined asFi=diagFi1,Fi2,��,FimFik=0or1,k=1,2,��,m(4)It is also assumed that, as shown in Figure 1, the measurement signals will be quantized before transmitting via the networks wherein data missing may occur.
The following logarithmic quantizer as proposed in [29] is applied,q(��)={��i��0if11+��q��i��0<�ԡ�11?��q��i��00if��=0?q(��)if��<0(5)where the parameter 0 < �� < 1 is termed as quantization density Inhibitors,Modulators,Libraries and��q=(1?��)/(1+��)(6)From [29], we can obtainq(��)=(I+��q)��(7)where ��q [?��q,��q] is a suitable model for the logarithmic quantizer q(��) with parameter ��q.Therefore, the faulty measurements together with quantization and the data transmission in the networks can be described byycFi(k)=��(I+��q)yFi(k)+(1?��)(I+��q)yFi(k?1)(8)where �� R is a Bernoulli distributed white sequence with?(��=1)=?(��)=�ġ�?(��=0)=1??(��)=1?�ġ�Specifically, Inhibitors,Modulators,Libraries if �� = 1, the quantized signal (I + ��q)yFi(k) is successfully transmitted, otherwise the transmission fails, i.e., the phenomenon of data missing.Remark 3The description of data transmission (8) was introduced in [30].
It can be seen that the output y(k) of the system Inhibitors,Modulators,Libraries model AV-951 is (I + ��q)yFi(k) with probability at k-th sampling time, and the value (I + ��q)yFi(k ? 1) with probability 1 ? Obviously, if the binary stochastic variable �� takes the value 0 consecutively at different sample times, the consecutive data missing would occur.In this paper, the following reliable filter is constructed:x?(k+1)=Afx?(k)=BfycFi(k)z?(k)=Cfx?(k)(9)where Af, Bf and Cf are filter parameters to be designed.Denoting ��(k) = [xT(k) x^T(k)]T and e(k) = z(k) �C (k), then the filtering error system for the ith fault mode can be described by the following two subsystems.S1: No packet dropout occurs.��(k+1)=A1i��(k)+A1di��(k?1)+?ww(k)+?siysi(k)e(k)=C��(k)S2: Packet dropout occurs.
��(k+1)=A2i��(k)+A2di��(k?1)+?ww(k)+?siysi(k)e(k)=C��(k)where[A1i|A1di|A2i|A2di]=[A0Bf(I+��q)FiCAf|0000|A00Af|00Bf(I+��q)FiC0][?w|?si]=[B0|0Bf(I+��q)(I?Fi)]C=[E?Cf]Due to packet drop-out, the filtering error system can be seen as combined by subsystem S1 and S2, which can be lumped into the following discrete time-delay switched system:��(k+1)=A��ki��(k)+A��kdi��(k?1)+?ww(k)+?siysi(k)e(k)=C��(k)(10)where selleck kinase inhibitor ��k is switching signal with ��k = 1, 2 being a piecewise constant function.Next, we will discuss how to design the filter parameters Af, Bf and Cf. In order to formulate the problem clearly, the following definitions are first given.Definition 4.