Delay range‐and‐rate dependent stability criteria for systems with interval time‐varying delay via a quasi‐quadratic convex framework

Abstract

Summary This paper concerns the stability analysis of systems with interval time‐varying delay. A Lyapunov‐Krasovskii functional containing an augmented quadratic term and certain triple integral terms is constructed to integrate features of the truncated Bessel‐Legendre inequality less conservative than Wirtinger inequality that encompasses Jensen inequality, respectively, and to exploit merits of the newly developed double integral inequalities tighter than auxiliary function‐based, Wirtinger, and Jensen double integral inequalities. A new quadratic convex lemma is proposed to derive delay and its derivative dependent sufficient stability conditions in terms of linear matrix inequalities synthetically with reciprocal convex approach and affine convex combination. The efficiency of the presented method is illustrated on some classical numerical examples.

A survey of inequality techniques for stability analysis of time‐delay systems

“…[15][16][17][18] Stability is a fundamental issue for time-delay systems, which has been extensively investigated during the last decades. [19][20][21][22][23][24][25][26][27][28][29][30][31] There are two main approaches to stability analysis of time-delay systems: frequency-domain approach and time-domain approach. In frequency-domain approach, the eigenvalues of a system matrix are calculated to study the stability of time-delay systems.…”

“…Stability is a fundamental issue for time‐delay systems, which has been extensively investigated during the last decades 19‐31 . There are two main approaches to stability analysis of time‐delay systems: frequency‐domain approach and time‐domain approach.…”

Stability Results of Thermal Control System with Time-Dependent Delays and Perturbations of Nonlinearity

“…e following are stability requirements stated as a collection of solved LMI conditions, which are indicated as a pair of solvable LMI conditions (Stability criteria) [10]. e newer delay time-bound conditions of stability, which favor long-term characteristics, mostly depend on the kind of LK function employed in the study; they avoid the restrictive commutative condition and choose a Lyapunov function of a more general form, and a new design algorithm, which takes into account the relation between the feedback control gains and the observer and improved EID estimator gains, is developed for the nonlinear system and clear relation between the developed estimator and the GESO is also clarified [11]. Novel iterative algorithms based on optimization are developed to solve the continuous-time and discrete-time Sylvester matrix equations [12].…”

Robust (Q, S, R)‐γ‐dissipative control of Takagi–Sugeno fuzzy systems with interval time‐varying delay and sampling

“…It is interesting to note that delay is usually the source of oscillation or instability in many practical models. Hence performances of delay systems have been explored and considered by many researchers 1–4 . It is also well known that the physical plants always contain some severe nonlinear structures in many physical models.…”

“…The main purpose about $$$ {H}_{\infty } $$$ performance and control were applied to improve the disturbance attenuation and stability of closed‐loop feedback system 7,8,12–14,16,17 . And passive performance will be a promising approach to remain internal stability of systems under consideration 4 . Furthermore, $$$ {H}_2 $$$ performance of systems can be used to minimize the dynamics for the given initial condition 3,8,20 .…”