Simultaneous stabilization with fixed closed-loop characteristic polynomial

Emre, E.

doi:10.1109/tac.1983.1103146

Cited by 38 publications

(8 citation statements)

References 2 publications

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“…form a right coprime factorization over R ps of system (9). The proper and stable rational matrix U(z) of dimensions m × m whose inverse exists and is also proper and stable is called biproper and bistable.…”

Section: Basic Concepts and Preliminary Resultsmentioning

confidence: 99%

“…Lemma 1. Let D(z) and N(z) be a right coprime factorization over R ps of system (9). Then there exists a proper and stable controller (4) that stabilizes system (9) if and only if the matrix [D(z) + F(z)N(z)] is biproper and bistable.…”

Section: Basic Concepts and Preliminary Resultsmentioning

confidence: 99%

“…In [9], has been derived a sufficient condition for the simultaneous stabilization of a finite number of single variable linear systems. In [10] and [11] iterative procedures are given for the computation of a strictly proper and stable controller that simultaneously stabilizes a finite set of strictly proper and minimum phase single variable and multivariable systems which have the same high frequency sign.…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous exact model matching with stability by output feedback

Kiritsis

2017

Journal of Electrical Engineering

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In this paper, is studied the problem of simultaneous exact model matching by dynamic output feedback for square and invertible linear time invariant systems. In particular, explicit necessary and sufficient conditions are established which guarantee the solvability of the problem with stability and a procedure is given for the computation of dynamic controller which solves the problem.K e y w o r d s: simultaneous model matching, output feedback, stability

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Section: Basic Concepts and Preliminary Resultsmentioning

confidence: 99%

Section: Basic Concepts and Preliminary Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simultaneous exact model matching with stability by output feedback

Kiritsis

2017

Journal of Electrical Engineering

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“…Finite descriptions of uncertainty appear naturally in practical situations. For example, the systems may represent a nominal system and many of its failed modes [1], a system that has several operating points [2] or a multivariable system with possible loss of sensors or actuators [3]. We refer Manuscript the reader to the monograph by Ackermann [2] for many more illustrative examples of applications of simultaneous stabilization.…”

Section: Introductionmentioning

confidence: 99%

Design of Simultaneously Stabilizing Controllers and Its Application to Fault-Tolerant Lane-Keeping Controller Design for Automated Vehicles

Suryanarayanan

Tomizuka

Suzuki

2004

IEEE Trans. Contr. Syst. Technol.

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Simultaneous stabilization deals with the following question: given a finite number of LTI plants 1 2 does there exist a single LTI controller such that each of the feedback interconnections ( ) ( = 1 2) is internally stable? This paper presents a new methodology for the design of simultaneously stabilizing controllers for two or more plants that satisfy a sufficient condition. A classic result from simultaneous-stability theory is invoked to cast the sufficient condition as a linear matrix inequality (LMI). It is shown that in this setting, the problem of design of simultaneously stabilizing controllers can be reduced to that of a standard control problem. The technique developed is applied to the design of a fault-tolerantcontroller for lane-keeping control of automated vehicles. The controller makes the system insensitive to a failure in either one of two lateral error measuring sensors used for lane-keeping control. Experimental results confirm the efficacy of the design and reinforce analytical predictions of performance.

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“…Such approaches had focus in two main areas. The first deals with the solution to the simultaneous stabilization problem itself, in which the solution to the problem has been tackled from a number of different directions, including polynomial [7][8][9], minimum phase [10], pole placement [11], system inversion [12], and optimization-based [13][14][15] approaches, respectively. The second deals with performance improvement for the simultaneous stabilization, or simultaneous optimal control, in which nonlinear optimization algorithms have been proposed [16][17][18][19].…”

mentioning

confidence: 99%

Decomposition-Based Simultaneous Stabilization with Optimal Control

Perez

Liu

Behdinan

2008

Journal of Guidance, Control, and Dynamics

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Simultaneous stabilization addresses the stability of multiple plants under a single feedback controller. It is desired for aircraft flight control operating under different conditions, when they are represented by a collection of linear dynamic models. The single controller brings continuity and a level of reliability. This paper presents a decomposition approach for the solution to the simultaneous stabilization problem. A bilevel design optimization architecture is adopted in which design of each individual plant (flight condition) is taking place at the bottom level, and the top-level optimization aims for single-control convergence of those individual controllers. Furthermore, performance requirements can be taken into account concurrently with the stabilization process, thanks to the separate bilevel decomposition concept. The effectiveness of the proposed approach is illustrated by different aircraft control system design test cases. Nomenclaturefeedback control gain p = roll rate, rad/s q = pitch rate, rad/s r = yaw rate, rad/s T e = elevator time constant, s t = time, s u = control vector w = vertical velocity, ft/s x = state vector x = local design variable y = output vector y = coupling design variable z = global design variable = sideslip, rad u = aircraft velocity, ft/s = pitch angle, rad = deflection, rad = eigenvalue = roll angle, rad ! = weighting factor Subscripts a = aileron e = elevator j = jth plant r = rudder SL = system level

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Simultaneous stabilization with fixed closed-loop characteristic polynomial

Cited by 38 publications

References 2 publications

Simultaneous exact model matching with stability by output feedback

Simultaneous exact model matching with stability by output feedback

Design of Simultaneously Stabilizing Controllers and Its Application to Fault-Tolerant Lane-Keeping Controller Design for Automated Vehicles

Decomposition-Based Simultaneous Stabilization with Optimal Control

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