PooGyeon Park

Delay-dependent robust stabilization of uncertain state-delayed systems

This paper concerns a problem of robust stabilization of uncertain state-delayed systems. A new delay-dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities. An algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties.

Reciprocally convex approach to stability of systems with time-varying delays

Whereas the upper bound lemma for matrix cross-product, introduced by Park (1999) and modified by Moon, Park, Kwon, and Lee (2001), plays a key role in guiding various delay-dependent criteria for delayed systems, the Jensen inequality has become an alternative as a way of reducing the number of decision variables. It directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities, resulting in a linear combination of positive functions weighted by the inverses of convex parameters. This paper suggests the lower bound lemma for such a combination, which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables, comparable to those based on the Jensen inequality lemma.

A delay-dependent stability criterion for systems with uncertain time-invariant delays

This paper provides a new stability criterion for systems with time-invariant uncertain delays. Based on an improved upper bound for the inner product of two vectors, a new delay-dependent robust stability criterion is derived, which is shown by an example less conservative than existing stability criteria.

Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems

Abstract Finding integral inequalities for quadratic functions plays a key role in the field of stability analysis. In such circumstances, the Jensen inequality has become a powerful mathematical tool for stability analysis of time-delay systems. This paper suggests a new class of integral inequalities for quadratic functions via intermediate terms called auxiliary functions, which produce more tighter bounds than what the Jensen inequality produces. To show the strength of the new inequalities, their applications to stability analysis for time-delay systems are given with numerical examples.

Delay-Dependent Robust Stabilization of Uncertain Time-Delay Systems

Abstract This paper concerns robust stabilization of uncertain time-delay systems. An improved upper bound for the inner product of two vectors is introduced, and used to derive new delay-dependent robust stability and stabilization conditions. An algorithm is also proposed to construct a robust stabilizing controller with a supoptimal maximal delay such that the system can be stabilized with the controller for all admissible uncertainties. It is illustrated by numerical examples that the proposed delay-dependent controller can be less conservative than existing results and it is even possible to capture the delay-independent stabilizability of the system.

A receding horizon Kalman FIR filter for discrete time-invariant systems

A receding horizon Kalman FIR filter is presented that combines the Kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown. The suggested filter is a FIR filter form which has many good inherent properties. It can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state. The suggested filter can be represented in either an iterative form or a standard FIR form. It is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition. The validity of the suggested filter is illustrated by numerical examples.

Technical Communique: Robust stabilization of uncertain input-delayed systems using reduction method

This paper concerns a robust stabilization problem that arises when applying the so-called reduction method to multiple input-delayed systems with parametric uncertainties. A robust stabilizing controller that can be constructed easily by solving convex problems in terms of linear matrix inequalities is presented. Numerical examples are provided to show that in many cases the proposed controller is less conservative and easier to obtain than the existing controllers.

H/sub /spl infin// state-feedback controller design for discrete-time fuzzy systems using fuzzy weighting-dependent Lyapunov functions

For discrete-time Takagi-Sugeno (TS) fuzzy systems, we propose an H/sub /spl infin// state-feedback fuzzy controller associated with a fuzzy weighting-dependent Lyapunov function. The controller, which is designed via parameterized linear matrix inequalities (PLMIs), employs not only the current-time but also the one-step-past information on the time-varying fuzzy weighting functions. Appropriately selecting the structures of variables in the PLMIs allows us to find an LMI formulation as a special case.

Fault diagnosis of a power transformer using an improved frequency-response analysis

A transformer is one of the most important units in power networks; thus, fault diagnosis of transformers is quite significant. In this paper, the frequency-response analysis, deemed as a suitable diagnostic method for electrical and/or mechanical faults of a transformer, is employed to make a decision over a defective phase. To deal with wideband frequency responses of each phase, a synthetic spectral analysis is proposed, which augments low- and medium-frequency components, and equalizes the frequency intervals of a resulting combined curve by a log-frequency interpolation. Furthermore, for discriminating a defective phase through computing overall amounts of deviation with other phases, the two well-known criteria and three proposed criteria are examined with experiment data. The overall diagnosis results show that the proposed criterion discriminates a defective phase with the highest average hit ratio among all of the provided criteria for selected faults.

Constrained MPC algorithm for uncertain time-varying systems with state-delay

In this note, we present a model predictive control (MPC) algorithm for uncertain time-varying systems with input constraints and state-delay. Uncertainty is assumed to be polytopic, and delay is assumed to be unknown but with a known upper bound. For a memoryless state-feedback MPC law, we define an optimization problem that minimizes a cost function and relaxes it to two other optimization problems by finding an upper bound of the cost function. One is solvable and the other is not. We prove equivalence and feasibilities of the two optimization problems under a certain assumption on the weighting matrix. Based on these properties and optimality, we show that feasible MPC from the optimization problems stabilizes the closed-loop system. Then, we present an improved MPC algorithm that includes relaxation procedures of the assumption on the weighting matrix and stabilizes the closed-loop system. Finally, a numerical example illustrates the performance of the proposed algorithm.