Simple algebraic criteria for stability of neutral delay-differential systems

Stability analysis for a class of neutral systems with mixed delays and sector-bounded nonlinearity

“…where A, A 1 , D, B, C follow the same definitions of those as in (1). The parameter uncertainties are assumed to be of the form of…”

“…There are two types of time delay systems, namely, retarded type and neutral type [12,14,15]. The retarded type system holds delays only in its states, while the neutral type one holds delays both in its states and in the derivative of its state [1,2,4,8,21,26]. Some new control technologies, like repetitive control, use the neutral type by the insertion of an artificial neutral delay into control loop for boosting the control performance of periodic signals [10].…”

The Applications of Algebraic Methods on Stable Analysis for General Differential Dynamical Systems with Multidelays

“…For (4) and 5, dynamic behaviors have been well studied by many researchers, and the theory of stability has been well known and discussed for decades in a wide range of literature; see [9][10][11][12][13][14][15]. But for linear neutral delayed system (4) or (5), the necessary and sufficient stability conditions are scarce and less efficient than their counterparts for retarded systems (1) and (3).…”

Further results on asymptotic stability of linear neutral systems with multiple delays

“…Since the existence of time delays is frequently the source of instability, the problem of stability analysis of such systems has received considerable attention and has been one of the most interesting topics in control theory. In terms of the determination of eigenvalues, measures and norms of matrices, or spectral radius of modulus matrices, the characteristic equation approach has been employed to investigate the problem of stability of system (1) with a single delay (see, for example, [1][2][3][4][5][6][7]). Based on the Lyapunov theory, sufficient conditions (delay-independent or delay-dependent) for asymptotic stability of neutral systems have been reported in terms of the linear matrix inequalities (LMIs) in the literature, such as Lien [8], Niculescu [9] and Han [10].…”