Taking the system coefficients as parameters, explicit expressions for the first 11 quasi-Lyapunov constants are deduced.
However, most of the results on the absolute stability of Lurie systems require that the system coefficients be bounded.
The conditions do not require analytical solutions but only bounds and an appropriate norm space assumption for uncertainties of the system coefficients matrix.
In this paper a population based evolutionary optimization methodology called firefly algorithm (FFA) is applied for the optimization of system coefficients of the infinite impulse response (IIR) system identification problem.
In the extended system, the state variable matrix Z, the system coefficient matrix M, the driven matrix N, and the output matrix O were defined as Z = x x ˙ ω = X ω M = A 11 A 21 0 A 12 A 22 0 D 11 D 21 0 N = 0 1 / m 0 = B 0 O = 1 0 0 = C 0. (8).
As depicted in Figure 2, system (5) is asymptotically stable even though the system coefficients are unbounded.
The states and system coefficients equations can then be summarized as: (4) The last two equations determine the current system coefficients, which will be appended to the system state.
The system coefficient matrix obtained from the finite-element method is often sparse and smaller in size by a factor of 12 to 16, compared to the linear-algebraic technique.
The predicted value of collector fluid temperature is used as an input in a companion model that, using the second law, predicts the system coefficient of performance (COP) from the known values of condensing temperature, compressor efficiency and refrigerant properties.
The system coefficient of performance (COP) at the design condition is 0.68, and the sensible heat ratio (SHR) for the dehumidifier lies in the range between 0.3 and 0.5 under different climatic, operating and design conditions.
The novelty of the paper can be summarised as follows: The elements of the system coefficient matrices can be unbounded functions; and also the time delay can be very large if its time derivative is less than one.
