In Eq. (4), (varvec{D}_{text{d}}) and (varvec{D}_{text{dir}}^{ k)}) are, respectively, the dynamic stiffness matrix of the FE model and the direct field dynamic stiffness matrix of subsystem k.
In addition, the method does not require a Hurwitz convex combination of the dynamic matrices of the subsystems.
Then the mobility matrices of the subsystems are derived, thereby a general mathematical description of this combined active passive model is realized.
We conduct the stability analysis of such T S fuzzy models using the Lie algebra LA generated by the Al matrices of these subsystems for each rule in the rule base.
We provide an LMI solution that does not require invertibility of the input matrices of each subsystem.
The number of subspaces and the variable matrices of each subsystem are indicated by s and θ i ∈ R (n + 1) × p , i = 1, 2, …, s, respectively.
Then the Lyapunov functional approach is applied to development of two stability conditions (Theorems 1 and 2), which are used to design filters and triggering matrices of each subsystem simultaneously.
where n 1 = 1, n 2 = 2, y k − 1) = v k − 1), and x(k) = [v k − 1) e ω (k − 1) e ω (k − 2)] T. So, the identification problem consists of finding variable matrices of each subsystem θ i = [1 a i b i ] T for PWARX systems (29) and estimating the regions of electrical current X i.
It is shown that the information matrices of maximal parameter subsystems in linear models are linear functions of the moment matrices.
The key idea of the method consists in minimizing a non-smooth ℓ2-norm-based weighted cost functional, constructed from the matrices of all the subsystems regardless of when each of them is active.
An elegant LMI solution to the problem is provided in (Siljak and Stipanovic 2001), but the method requires that the input matrix of each subsystem be invertible, i.e., each subsystem has as many independent control inputs as state variables.
