In the special case of ((0,1 -matrices, the inequality (9) reduces to the following Khinchin-type inequality: msum_{i=1}^{m}r_{i}^{2} + nsum_{j=1}^{n}c_{j}^{2} leqsigma^{2} +mnsigma, (10,1 -matrices}), (c_{i}), and σ denotherow sums, column sums, and entrinequalityg of an (mtimes n) ((0,1)) matrix, respectively, as presented by Matúš and Tuzar [3].
This is a matrix version of the inequality (1.4).
The matrix inequality of the BRL is nonlinear because of multiplication of the variable of Lyapunov equation and gains of controller.
The matrix inequality ≽ shows the positive semi-definiteness.
Furthermore, based on the lower and upper bounds of the time-varying transition rates, and by using the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition on SSH∞FTB of closed-loop system is presented.
By using the Lyapunov Krasovskii function and the linear matrix inequality (LMI), the stability of the finite-time H∞ adaptive fault-tolerant controller is theoretically proved.
The gain of the observer is designed by applying the cone complementary linearization method to the matrix inequality.
Then, based on the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition is presented, which guarantees the estimation error systems are stochastically admissible and achieve a prescribed H∞ noise attenuation performance index.
The consensus problem is reduced to solve the matrix inequality problem under actuator saturation.
Using the technique of the bilinear matrix inequality (BMI), the necessary and sufficient conditions are given for interconnected stability and cooperative stabilization of two subsystems.
