Abstract. The function that maps a positive semidefinite matrix to the trace of one of its nonnegative integer power is semidefinite representable. In this note, we reduce the size of this semidefinite representation from O(kn) linear matrix inequalities of dimension n, where k is the desired power and n× n the size of the matrix to O(log 2 (k)) linear matrix inequalities of dimension 2n. We al...

This paper is concerned with the problem of synchronization for complex dynamic networks with state and coupling time-delays. Therefore, larger class and more complicated complex dynamic networks can be considered for the synchronization problem. Based on the Lyapunov-Krasovskii functional, a delay-independent criterion is obtained and formulated in the form of linear matrix inequalities (LMIs)...

Matrix inequalities have come to be extremely important in systems engineering in the past decade. This is because many systems problems convert directly into matrix inequalities. Matrix inequalities take the form of a list of requirements that polynomials or rational functions of matrices be positive semide nite. Of course while some engineering problems present rational functions which are we...

This paper considers the robust fault detection and isolation (FDI) problem for uncertain linear timeinvariant (LTI) systems. An FDI filter minimizes the sensitivity of the residual signal to disturbances and modeling errors subject to the constraint that the transfer matrix function from the faults to the residual is close to a diagonal matrix (for fault isolation). A solution of the optimizat...

This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

The paper establishes the design procedure for the state feedback control of linear discrete-time systems, considerable as an interposed design criterium in the form of linear matrix inequalities. The goal is to design the feedback control which guarantees bounded H2 performance index for the system transfer function matrix and H∞ norm attenuation for the disturbance transfer function matrix, b...