Strong stability radii of positive linear time-delay systems

Abstract

SUMMARYIn this paper, we study robustness of the strong delay-independent stability of linear time-delay systems under multi-perturbation and affine perturbation of coefficient matrices via the concept of strong delayindependent stability radius (shortly, strong stability radius). We prove that for class of positive time-delay systems, complex and real strong stability radii of positive linear time-delay systems under multiperturbations (or affine perturbations) coincide and they are computed via simple formulae. Apart from that, we derive solution of a global optimization problem associated with the problem of computing of the strong stability radii of a positive linear time-delay system. An example is given to illustrate the obtained results.

Decay rate constrained stabilization of positive systems using static output feedback

“…To find a controller (5) such that the closed-loop system converges as fast as possible, Theorem 2 indicates that we need to look for the largest feasible positive scalar >0 such that the linear matrix inequalities (11), (12) and the matrix equality (8) have solution consisting of diagonal matrices P>0,Q>0, scalar ε>0 and matrixL. The optimized decay rate can be obtained by solving the…”

“…In recent years, especially, positive systems have drawn much attention of control theorists and many fundamental and important results have been obtained, see [1][2][3][4][5], and references therein. Among them major efforts are devoted to the behavioral analysis and property characterization such as the stability [6][7][8][9][10][11], realizability [12][13][14] and reachability/controllability [15][16][17] of positive systems.…”

On Positive Linear Volterra-Stieltjes Differential Systems

“…These results have been extended recently to many various classes of positive systems such as positive linear time-delay differential systems, see e.g. [29], [31], [43], positive linear discrete time-delay systems, see e.g. [16], [28] and positive linear functional differential systems, see e.g.…”

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“…Moreover, in general, obtained results of problems for class of positive systems are often very interesting, see e.g. [1], [6], [8]- [9], [11], [12]- [14], [18], [19].…”