摘要:

AbstractQuantitative feedback theory (QFT) has presented techniques for the design of multiple‐input‐multiple‐output (MIMO) linear time invariant (LTI) systems with structured parameter uncertainty in the plantPfor the satisfaction of specifications on the closed loop transfer function matrixT= [Tij]. In many practical applications the specifications are of the basically non‐interacting (BNIA) type, i.e.aii(ω)<|Tii(jω) |

ISSN:1049-8923    

DOI:10.1002/rnc.4590030402

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractThe purpose of this paper is to construct Lyapunov functions to prove the key fundamental results of linear system theory, namely, the small gain (bounded real), positivity (positive real), circle, and Popov theorems. For each result a suitable Riccati‐like matrix equation is used to explicitly construct a Lyapunov function that guarantees asymptotic stability of the feedback interconnection of a linear time‐invariant system and a memoryless nonlinearity. Lyapunov functions for the small gain and positivity results are also constructed for the interconnection of two transfer functions. A multivariable version of the circle criterion, which yields the bounded real and positive real results as limiting cases, is also derived. For a multivariable extension of the Popov criterion, a Lure‐Postnikov Lyapunov function involving both a quadratic term and an integral of the nonlinearity, is constructed. Each result is specialized to the case of linear uncertainty for the problem of robust stability. In the case of the Popov criterion, the Lyapunov function is a parameter‐dependent quadratic Lyapunov f

ISSN:1049-8923    

DOI:10.1002/rnc.4590030403

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractThe key problems addressed and solved in the framework of time‐invariant continuous‐time multiple‐input multiple‐output (MIMO) linear systems are the following: (a) the necessary and sufficient condition on the system under which there exists a control that can force the system to exhibit a requested tracking property without using any information about the mathematical description of the system internal dynamics and external disturbances; (b) the synthesis of an output error algorithm expressing stablewise tracking with finite (pre‐specified) reachability time; (c) the synthesis of a Proportional‐Derivative (PD) control algorithm for stablewise tracking with finite (given) reachability time without utilizing a mathematical model of the system internal dynamics, its state and the unmeasured, unknown time‐varying disturbances. Simulation results illustrate the theory with an unstable MIMO system under different desired stablewise tracking s

ISSN:1049-8923    

DOI:10.1002/rnc.4590030404

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

ISSN:1049-8923    

DOI:10.1002/rnc.4590030401

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY