Relaxed inequality approach to robust ℋ _∞ stability analysis of discrete-time systems with time-varying delay

Abstract

This study aims at deriving a less conservative delay-dependent criterion for the robust H ∞ stability analysis of discrete-time systems with interval time-varying state delay. To this end, an appropriate Lyapunov-Krasovskii functional containing triple summation terms is established and a relaxed inequality approach is proposed to address the induced double summation inequality and to exploits novel relaxation variables for null sum terms. Three numerical examples are provided to illustrate the effectiveness of the derived stability criteria.

Stability analysis of discrete-time systems with time-varying delays: generalized zero equalities approach

“…Example Consider the system with For various h 1 , Table shows the allowable upper bound of h ( k ) that guarantees the asymptotic stability of . From Table , we can see that the proposed stability criteria in Corollary and Theorem can produce the upper bound h 2 better than those obtained in . Further, by comparing Theorem and Corollary , one can see that the generalized zero equalities effectively reduce the conservatism of the stability criteria only with a little increment of the number of variables .…”

“…In such circumstances, techniques handling several summation terms derived from the forward difference of a Lyapunov–Krasovskii functional are a key point to obtain the tighter upper bound. Thus, many methods have been proposed, such as a slack matrix‐based inequality , the free‐weighting matrix method , Jensen inequality , a lower bound lemma for reciprocal convexity, and zero equalities approach . Among the methods, Jensen inequality has been frequently used in most recent papers for discrete‐time‐delay systems because it requires fewer decision variables than the other approaches with comparable performance.…”

Polynomials‐based summation inequalities and their applications to discrete‐time systems with time‐varying delays

“…It completes the proof. When the zero-order to second-order orthogonal polynomial functions (17) are utilized, a more flexible summation inequality is obtained as follows.…”

“…Because mathematical techniques deriving lower bounds of summation quadratic functions are crucial to derive less conservative stability criteria, inequality with slack matrices [9,10] and Jensen inequality [7,[11][12][13][14][15] have been utilized. Further, with the summation inequalities, a lower bound lemma for reciprocal convexity [14,16], zero equality approaches [14,17,18], and a delay-partitioning method [19,20] have been used to reduce the conservatism of stability criteria for discrete-time systems with time-varying delays. Among the methods, the Jensen inequality has been frequently used because of its compactness.…”

Delay‐Dependent Stability Criterion for Discrete‐Time Systems with Time‐Varying Delays

“…So the stability analysis of time-delay systems is of theoretical and practical importance. A great amount of research and results are dedicated to the development of the stability analysis of time-delay systems, see, for example, [1][2][3][4], and references therein. On the other hand, most practical systems take digital computers (usually microprocessors or microcontrollers) with the necessary input/output hardware to complete the systems, the stability analysis of discrete-time systems has been one of the hot issues in the control community, see [5][6][7][20][21][22][23][24][25][26][27].…”