• Transactions on Control, Automation and Systems Engineering
• /
• v.4 no.4
• /
• pp.324-329
• /
• 2002

In this paper, the guaranteed cost filtering design method for linear time delay systems with convex bounded uncertainties in discrete-time case is presented. The uncertain parameters are assumed to be unknown but belonging to known convex compact set of polytotype less conservative than norm bounded parameter uncertainty. The main purpose is to design a stable filter which minimizes the guaranteed cost. The sufficient condition for the existence of filter, the guaranteed cost filter design method, and the upper bound of the guaranteed cost are proposed. Since the proposed sufficient conditions are LMI(linear matrix inequality) forms in terms of all finding variables, all solutions can be obtained simultaneously by means of powerful convex programming tools with global convergence assured. Finally, a numerical example is given to check the validity of the proposed method.

• Proceedings of the Korean Society For Composite Materials Conference
• /
• 2001.05a
• /
• pp.155-158
• /
• 2001

The layup optimization by genetic algorithm (GA) for the strength of laminated composites with free-edge is presented. For the calculation of interlaminar stresses of composite laminates with free edges, extended Kantorovich method is applied. In the formulation of GA, repair strategy is adopted for the satisfaction of given constraints. In order to consider the bounded uncertainty of material properties, convex modeling is used. Results of GA optimization with scattered properties are compared with those of optimization with nominal properties. The GA combined with convex modeling can work as a practical tool for light weight design of laminated composite structures since uncertainties are always encountered in composite materials.

• Proceedings of the Korean Society For Composite Materials Conference
• /
• 2001.10a
• /
• pp.70-73
• /
• 2001

The layup optimization by genetic algorithm (GA) for the interlaminar strength of laminated composites with free edge is presented. For the calculation of interlaminar stresses of composite laminates with free edges, extended Kantorovich method is applied. In the formulation of GA, repair strategy is adopted for the satisfaction of given constraints. In order to consider the bounded uncertainty of material properties, convex modeling is used. Results of GA optimization with scattered properties are compared with those of optimization with nominal properties. The GA combined with convex modeling can work as a practical tool for maximum interlaminar strength design of laminated composite structures, since uncertainties are always encountered in composite materials and the optimal results can be changed.

• Journal of Institute of Control, Robotics and Systems
• /
• v.19 no.6
• /
• pp.489-494
• /
• 2013

This paper tackles the problem of designing a dynamic output-feedback control for linear discrete-time norm-bounded uncertain systems with input saturation. By employing a LPV (Linear Parameter Varying) instead of LTI (Linear Time-Invariant) control, the useful information on interpolation parameters appearing in the procedure of representing saturation nonlinearity as a convex polytope is additionally applied in the control design procedure. By solving the addressed problem that can be recast into a convex optimization problem characterized by LMIs (Linear Matrix Inequalities) with one prescribed scalar, the vertices of convex set containing an LPV output-feedback control gain and the associated maximal invariant set of initial states are simultaneously obtained.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.39 no.5
• /
• pp.26-33
• /
• 2002

The design method of robust $H_{\infty}$ filtering for discrete-time uncertain linear systems is investigated in this paper. The uncertain parameters are assumed to be unknown but belonging to known convex compact set of polytope type. The objective is to design a stable robust $H_{\infty}$ filter guaranteeing the asymptotic stability of filtering error dynamics and present an $L_2$ induced norm bound analytically for the modified $H_{\infty}$ performance measure. The sufficient condition for the existence of robust $H_{\infty}$ filter and the filter design method are established by LMI(linear matrix inequality) approach, which can be solved efficiently by convex optimization. The proposed algorithm is checked through an example.

• 제어로봇시스템학회:학술대회논문집
• /
• 1992.10b
• /
• pp.575-580
• /
• 1992

Mixed H$_{2}$/H$_{\infty}$ robust control synthesis is considered for finite dimensional linear time-invariant systems under the presence of diagonal structured uncertainties. Such uncertainties arise for instance when there is real perturbation in the nominal model of the state space system or when modeling multiple (unstructured) uncertainty at different locations in the feedback loop. This synthesis problem is reduced to convex optimization problem over a bounded subset of matrices as well as diagonal matrix having certain structure. For computational purpose, this convex optimization problem is further reduced into Generalized Eigenvalue Minimization Problem where a powerful algorithm based on interior point method has been recently developed..

• Journal of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.775-795
• /
• 2011

The disturbance attenuation problem for a class of discretetime switched linear systems with exponential uncertainties via switched state feedback and switched dynamic output feedback is investigated, respectively. By using Taylor series approximation and convex polytope technique, exponentially uncertain discrete-time switched linear system is transformed into an equivalent switched polytopic model with additive norm bounded uncertainty. For such equivalent switched model, one designs its switching strategy and associated state feedback controllers and dynamic output feedback controllers so that whole switched model is asymptotical stabilization with H-in nity disturbance attenuation base on switched Lyapunov function and LMI approach. Finally, two numerical examples are presented to illustrate our results.

• Journal of Institute of Control, Robotics and Systems
• /
• v.1 no.1
• /
• pp.13-19
• /
• 1995

In this paper, generalized singular value is defined. Using the generalized singular value, robust stability conditions and robust pole placement conditions of structured uncertain systems with star shaped uncertainties are derived. Especially, norm bounded and polytopic uncertainty regions are considered as star shaped uncertainty regions. Linear matrix inequality problems are proposed in order to compute the upper bound of the generalized singular value. The proposed linear matrix inequality problems can be solved by using the convex optimization method.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.62.4-62
• /
• 2001

In this paper, we propose a delay-dependent guaranteed cost controller design method for uncertain linear systems with time delay. The uncertainty is norm bounded and time-varying. A quadratic cost function is considered as the performance measure for the given system. Based on the Lyapunov method, sufficient condition, which guarantees that the closed-loop system is asymptotically stable and the upper bound value of the closed-loop cost function is not more than a specied one, is derived in terms of Linear Matrix Inequalities(LMIs) that can be solved sufficiently. A convex optimization problem can be formulated to design a guaranteed cost controller, which minimizes the upper bound value of the cost function. Numerical examples show the activeness of the proposed method.

• International Journal of Control, Automation, and Systems
• /
• v.6 no.1
• /
• pp.15-23
• /
• 2008

This paper considers the problem of delay-dependent guaranteed cost controller design for uncertain neutral systems with distributed delays. The system under consideration is subject to norm-bounded time-varying parametric uncertainty appearing in all the matrices of the state-space model. By constructing appropriate Lyapunov functionals and using matrix inequality techniques, a state feedback controller is designed such that the resulting closed-loop system is not only robustly stable but also guarantees an adequate level of performance for all admissible uncertainties. Furthermore, a convex optimization problem is introduced to minimize a specified cost bound. By matrix transformation techniques, the corresponding optimal guaranteed controller can be obtained by solving a linear matrix inequality. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed approach.