Journal ArticleDOI
New results in 2D optimal control theory
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TLDR
An ℓ2-approach permits the optimal control problem to be reduced to a norm minimization one in Hilbert spaces and the singularities of the 2D Riccati equation are examined to characterize suboptimal control laws that apply whenever the solvability conditions are not satisfied.Abstract:
The infinite horizon optimal control problem is solved for 2D systems described by the Fornasini-Marchesini model. An l2-approach permits us to reduce the optimal control problem to a norm minimization one in Hilbert spaces. Both necessary and sufficient conditions for solvability and the structure of the solution are established. Moreover, a comparison with known results is presented, and the singularities of the 2D Riccati equation are examined in order to characterize suboptimal control laws that apply whenever the solvability conditions are not satisfied.read more
Citations
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Journal ArticleDOI
Two-Dimensional Dissipative Control and Filtering for Roesser Model
TL;DR: This paper investigates the problems of two-dimensional (2-D) dissipative control and filtering for a linear discrete-time Roesser model and proposes new designs of 2-D (Q, S, R)-α-dissipative filters of observer form and general form using a linear matrix inequality (LMI) approach.
Journal ArticleDOI
Brief H∞ control and robust stabilization of two-dimensional systems in Roesser models
TL;DR: A state-space solution for robust stabilization of 2-D systems subject to a class of norm bounded uncertainties is presented and an application example of stabilization of processes expressed in a Darboux equation is demonstrated.
Journal ArticleDOI
H ∞ and Robust Control of 2-D Systems in FM Second Model
TL;DR: It is shown that the design of output feedback controller can be recast into a convex optimization problem characterized by linear matrix inequalities (LMIs) and the LMI solution is further extended to solve the robust stabilization problem for 2-D systems subject to norm-bounded uncertainty.
Journal ArticleDOI
Stability and l1-gain analysis for positive 2D T-S fuzzy state-delayed systems in the second FM model
TL;DR: This paper considers the problems of delay-dependent stability and l"1-gain analysis for a class of positive two-dimensional (2D) Takagi-Sugeno (T-S) fuzzy linear systems with state delays described by the second FM model and proposes a co-positive type Lyapunov function method.
Journal ArticleDOI
Delay-dependent exponential stabilization of positive 2D switched state-delayed systems in the Roesser model
TL;DR: The design of positive state feedback controller under which the resulting closed-loop system meets the requirements of positivity and exponential stability is presented in terms of linear matrix inequalities (LMIs).
References
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Journal ArticleDOI
Stability analysis of 2-D systems
Ettore Fornasini,G. Marchesini +1 more
TL;DR: In this paper, a polynomial stability criterion for 2D systems is taken as a starting point for introducing a frequency dependent Lyapunov equation, and the Fourier coefficients are explicitly obtained as the sum of series involving the system matrices.
Journal ArticleDOI
State and output feedback stabilizability of 2-D systems
TL;DR: In this paper a controller theory is introduced for multivariable 2-D systems together with stabilization algorithms based on state and output feedback techniques.
Journal ArticleDOI
Controllability of 2-D systems
Paula Rocha,Jan C. Willems +1 more
TL;DR: The structure of state-space systems is analyzed, and the notions of trimness, reachability, and observability are introduced and characterized and these realizations do not depend on any assumptions concerning causality.
Journal ArticleDOI
Optimal control of 2-D systems
C. Li,M.S. Fadali +1 more
TL;DR: In this article, a generalized performance measure suited to 2D systems is introduced and the canonical equations associated with this performance measure and a general nonlinear model for 2D linear quadratic regulator problem are derived.
Journal ArticleDOI
Optimal control of two-dimensional systems
Mauro Bisiacco,Ettore Fornasini +1 more
TL;DR: In this article, necessary and sufficient conditions for the existence and uniqueness of the solution of the optimal control problem of discrete-time linear time invariant two-dimensional systems are determined.