Analysis and synthesis of dynamic systems with positive characteristics

• Main Author: Shen, Jun (Author)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer, 2017.
• Series: Springer theses.
• Subjects: Positive systems.; elektronické knihy; electronic books
• ISBN: 9789811038808; 9789811038792
• Physical Description: 1 online resource (xxiii, 123 pages)
• Abstract: This thesis is concerned with analysis and synthesis problems for several classes ofdynamic systems with positivity or a more general cone invariance. In terms of analysis, stability and performance characterizations are established for several types of dynamic systems with positivity or cone-invariant property. Specifically, the following four aspects are exploited: (a) For positive linear system with bounded or unbounded time-varying delays, it is theoretically proved that the'1=L1-gain is fully determined by the system matrices, while the time delays playno roles in the'1=L1-gain characterization. As an application example, it is shownthat the convergence rate analysis of containment control of multi-agent systemswith diverse communication delays can be cast as stability analysis of a corre-sponding positive system with multiple delays. (b) For a positive system withdistributed delays, it is shown that itsL1-gain is the same as that of a correspondingdelay-free positive system. Along this line, upper and lower bounds for theL1-gainof a positive system with distributed delays over a bounded time-varying intervalare also given. (c) For a linear delay system which is invariant with respect to ageneral proper cone, its asymptotic stability and cone-induced gain turn out to beinsensitive to the magnitude of time delays. (d) For a class of coupled differential-difference equations, necessary and sufficient conditions on the posi-tivity and asymptotic stability are presented. In terms of synthesis, several fundamental control problems are studied: (a) Thestatic output-feedback stabilization problem for positive systems is revisited. It ispointed out that for a class of positive systems whose output matrix has a particularrow echelon form, this problem can be completely solved via linear programming. By duality, this fact is also valid when the column echelon form of the input matrixhas a particular structure. Along this line, by augmenting the output matrix as wellas the feedback gain matrix, an iterative convex optimization algorithm is devel-oped for a general multi-input multi-output positive system. (b) The staticoutput-feedback stabilization problem with optimalL1-gain for positive linearsystems is addressed. It is shown that when the control input or the measured outputis a scalar, this problem can be directly solved via linear programming by adding aone-dimensional search. (c) TheH1model reduction problem of discrete-time positive linear systems with inhomogeneous initial conditions is investigated. A necessary and sufficient condition is established for the existence of a desiredreduced-order model such that the output error between the original system and thereduced-order one is bounded by a weighted sum of the magnitude of the input andthat of the initial condition. Moreover, based on congruent transformation and thedual form of bounded real lemma, several equivalent conditions are derived interms of linear matrix inequalities and an iterative convex optimization algorithm isdeveloped accordingly.
• Item Description: "Doctoral thesis accepted by the University of Hong Kong, Hong Kong."
• Access: Plný text je dostupný pouze z IP adres počítačů Univerzity Tomáše Bati ve Zlíně nebo vzdáleným přístupem pro zaměstnance a studenty

This thesis develops several systematic and unified approaches for analyzing dynamic systems with positive characteristics or a more general cone invariance property. Based on these analysis results, it uses linear programming tools to address static output feedback synthesis problems with a focus on optimal gain performances. Owing to their low computational complexity, the established controller design algorithms are applicable for large-scale systems. The theory and control strategies developed will not only be useful in handling large-scale positive delay systems with improved solvability and at lower cost, but also further our understanding of the system characteristics in other related areas, such as distributed coordination of networked multi-agent systems, formation control of multiple robots.