Efficient Low-PAR Waveform Design Method for Extended Target Estimation Based on Information Theory in Cognitive Radar

This paper addresses the waveform design problem of cognitive radar for extended target estimation in the presence of signal-dependent clutter, subject to a peak-to-average power ratio (PAR) constraint. Owing to this kind of constraint and the convolution operation of the waveform in the time domain, the formulated optimization problem for maximizing the mutual information (MI) between the target and the received signal is a complex non-convex problem. To this end, an efficient waveform design method based on minimization–maximization (MM) technique is proposed. First, by using the MM approach, the original non-convex problem is converted to a convex problem concerning the matrix variable. Then a trick is used for replacing the matrix variable with the vector variable by utilizing the properties of the Toeplitz matrix. Based on this, the optimization problem can be solved efficiently combined with the nearest neighbor method. Finally, an acceleration scheme is used to improve the convergence speed of the proposed method. The simulation results illustrate that the proposed method is superior to the existing methods in terms of estimation performance when designing the constrained waveform.

Aspects of non-commutative function theory

We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.

Passive Control of Switched Singular Systems via Output Feedback

An instrumental matrix approach to design output feedback passive controller for switched singular systems is proposed in this paper. The nonlinear inequality condition including Lyapunov inverse matrix and controller gain matrix is decoupled by introducing additional instrumental matrix variable. Combined with multiple Lyapunov function method, the nonlinear inequality is transformed into linear matrix inequality (LMI). An LMI condition is presented for switched singular system to be stable and passive via static output feedback under designed switching signal. Moreover, the conditions proposed do not require the decomposition of Lyapunov matrix and its inverse matrix or fixing to a special structure. The theoretical results are verified by means of an example. The method introduced in the paper can be effectively extended to a single singular system and normal switched system.

Improved RobustH∞Filtering Approach for Nonlinear Systems

An improved design approach of robustH∞filter for a class of nonlinear systems described by the Takagi-Sugeno (T-S) fuzzy model is considered. By introducing a free matrix variable, a new sufficient condition for the existence of robustH∞filter is derived. This condition guarantees that the filtering error system is robustly asymptotically stable and a prescribedH∞performance is satisfied for all admissible uncertainties. Particularly, the solution of filter parameters which are independent of the Lyapunov matrix can be transformed into a feasibility problem in terms of linear matrix inequalities (LMIs). Finally, a numerical example illustrates that the proposed filter design procedure is effective.

A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming

Based on the semidefinite programming relaxation of the binary quadratic programming, a rank-two feasible direction algorithm is presented. The proposed algorithm restricts the rank of matrix variable to be two in the semidefinite programming relaxation and yields a quadratic objective function with simple quadratic constraints. A feasible direction algorithm is used to solve the nonlinear programming. The convergent analysis and time complexity of the method is given. Coupled with randomized algorithm, a suboptimal solution is obtained for the binary quadratic programming. At last, we report some numerical examples to compare our algorithm with randomized algorithm based on the interior point method and the feasible direction algorithm on max-cut problem. Simulation results have shown that our method is faster than the other two methods.

Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties

This paper considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems with convex polytopic uncertainties. The stability condition of the fractional-order linear time-invariant systems without uncertainties is extended by introducing a new matrix variable. The new extended stability condition is linear with respect to the new matrix variable and exhibits a kind of decoupling between the positive definite matrix and the system matrix. Based on the new extended stability condition, sufficient conditions for the above robust stability and stabilization problems are established in terms of linear matrix inequalities by using parameter-dependent positive definite matrices. Finally, numerical examples are provided to illustrate the proposed results.