Continuous-time singular linear–quadratic control: Necessary and sufficient conditions for the existence of regular solutions

We study the λ-classification of absorbing birth-and-death processes, giving necessary and sufficient conditions for such processes to be λ-transient, λ-null recurrent and λ-positive recurrent.

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Positive fractional continuous-time linear systems with singular pencils

Bulletin of the Polish Academy of Sciences Technical Sciences ◽

10.2478/v10175-012-0002-0 ◽

2012 ◽

Vol 60 (1) ◽

pp. 9-12 ◽

Cited By ~ 11

Author(s):

T. Kaczorek

Keyword(s):

Linear Systems ◽

Continuous Time ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Descriptor Systems ◽

State Variables ◽

Algebraic Constraints ◽

Necessary And Sufficient ◽

Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

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On an infinite dimensional linear-quadratic problem with fixed endpoints: The continuity question

International Journal of Applied Mathematics and Computer Science ◽

10.2478/amcs-2014-0053 ◽

2014 ◽

Vol 24 (4) ◽

pp. 723-733

Author(s):

K.Maciej Przyłuski

Keyword(s):

Minimum Energy ◽

Sufficient Conditions ◽

Control Problems ◽

Linear Quadratic Control ◽

Linear Quadratic ◽

Minimum Norm Solution ◽

Quadratic Problem ◽

Infinite Dimensional ◽

Necessary And Sufficient ◽

Quadratic Control Problems

Abstract In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.

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Necessary and Sufficient Conditions on Quadratic Stablizability for Polytopic Uncertain Continuous-Time Switched Linear Systems

Communications in Computer and Information Science - Control and Automation ◽

10.1007/978-3-642-10741-2_1 ◽

2009 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Naohisa Otsuka ◽

Takuya Soga

Keyword(s):

Linear Systems ◽

Continuous Time ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Switched Linear Systems ◽

Necessary And Sufficient

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Linear-quadratic optimization and some general hypotheses on optimal control

Mathematical Problems in Engineering ◽

10.1155/s1024123x9900109x ◽

1999 ◽

Vol 5 (4) ◽

pp. 275-289 ◽

Cited By ~ 2

Author(s):

L. I. Rozonoer

Keyword(s):

Optimal Control ◽

Initial Data ◽

Optimization Problem ◽

Sufficient Conditions ◽

Quadratic Optimization ◽

Necessary And Sufficient Conditions ◽

Maximum Condition ◽

Linear Quadratic ◽

Existence Of Optimal Control ◽

Necessary And Sufficient

Necessary and sufficient conditions for existence of optimal control for all initial data are proved forLQ-optimization problem. If these conditions are fulfilled, necessary and sufficient conditions of optimality are formulated. Basing on the results, some general hypotheses on optimal control in terms of Pontryagin's maximum condition and Bellman's equation are proposed.

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Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm

Archives of Control Sciences ◽

10.2478/v10170-010-0044-1 ◽

2011 ◽

Vol 21 (3) ◽

pp. 287-298 ◽

Cited By ~ 16

Author(s):

Tadeusz Kaczorek

Keyword(s):

Linear Systems ◽

Continuous Time ◽

Equivalent Form ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Descriptor Systems ◽

State Equations ◽

Necessary And Sufficient ◽

Descriptor Linear Systems ◽

Time Linear

Checking of the positivity of descriptor linear systems by the use of the shuffle algorithmNecessary and sufficient conditions for the positivity of descriptor continuous-time and discrete-time linear systems are established. The shuffle algorithm is applied to transform the state equations of the descriptor systems to their equivalent form for which necessary and sufficient conditions for their positivity have been derived. A procedure for checking the positivity of the descriptor systems is proposed and illustrated by numerical examples.

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