Design method of dissipative filter of switching gene regulation and control network with random disturbance and time-varying delay
A gene regulation network and filter design technology, applied in the direction of single-port active network, can solve the problem that it is difficult to obtain the state value of the gene regulation network
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specific Embodiment approach 1
[0062] Specific implementation mode one: refer to figure 1 Specifically illustrate the present embodiment, the dissipative filter design method of the switched gene regulatory network with random disturbance and time-varying time delay described in the present embodiment, the method includes the following steps:
[0063] Step 1, designing the Lyapunov function according to the symmetrical positive definite matrix, the external disturbance input signal and the filtering error system, so that the filtering error system conforms to dissipation and mean square exponential stability;
[0064] Step 2: Obtain a full-order linear filter according to the piecewise Lyapunov function and the designed filter gain, and complete the design of the filter.
[0065] In this embodiment, figure 2 is an ideal gene regulatory network model. However, in the actual gene regulatory network model, there are often some external disturbances, time lags, and switching factors. In order to better and mo...
specific Embodiment approach 2
[0071] Specific implementation mode two: refer to figure 2 and image 3 This embodiment is described in detail. This embodiment is a further description of the dissipative filter design method of the switching gene regulation network with random disturbance and time-varying delay described in the first embodiment. In this embodiment, the filtering error The system is:
[0072]
[0073] In the formula, I is the identity matrix, A fi ,B fi ,C fi ,D fi , K f1i , K f2i is the filter gain, A i =A(α(t)),B i =B(α(t)),C i =C(α(t)),D i =D(α(t)),E ji =E j (α(t)),F ji =F j (α(t)),G ji =G j (α(t)),H ji =H j (α(t)),K ji = K j (α(t)),
[0074] The matrix A=diag{a1,a2,...,an} and C=diag{c1,c2,...,cn} are diagonal matrix, diag is the abbreviated symbol of diagonal matrix, diag{a1,a2, ...,an} represents the diagonal matrix where the main diagonal elements are a1, a2,...,an, and other positions are 0, ai>0, ci>0 represent the mRNA and protein of the i-th gene respect...
specific Embodiment approach 3
[0075] Specific embodiment three: This embodiment is a further description of the dissipative filter design method for switching gene regulatory networks with random disturbance and time-varying time-delay described in specific embodiment two. In this embodiment, the concentration of mRNA x m (t) is expressed as:
[0076] dx m (t)={-A(α(t))x m (t)+B(α(t))f(x p (t-τ(t)))+E 1 (α(t))v 1 (t)}dt+F 1 (α(t))x m (t)dω 1 (t) Formula 6,
[0077] protein concentration x p (t) is expressed as:
[0078] dx p (t)={-C(α(t))x p (t)+D(α(t))x m (t-σ(t))+E 2 (α(t))v 2 (t)}dt+F 2 (α(t))x p (t)dω 2 (t) Formula 7.
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