Tính ổn định và bền vững của một số tính chất hệ động lực tuyến tính

TÍNH ỔN ĐỊNH VÀ BỀN VỮNG CỦA MỘT SỐ TÍNH CHẤT HỆ ĐỘNG LỰC TUYẾN TÍNH DƯƠNG ĐẶNG XUÂN THÀNH Trang nhan đề Lời cảm ơn Lời cam đoan Mục lục Một số từ viết tắt Mở đầu Chương 1: Hệ liên tục có chậm Chương 2: Hệ rời rạc cao cấp Chương 3: Phương trình sai phân Chương 4: Vô hạn chiều Chương 5: Hữu hạn chiều Chương 6: Thuật toán tính toán Kết luận Danh mục công trình Tài liệu tham khảo Mục lục Danh sách ký hiệu v Lời mở đầu 1 Phần 1: Bán kính ổn định 9 Chương 1 Hệ liên tục có châm 10 1.1 Toán tử Metzler 11 1.2 Tính ổn định của hệ dương và tựa đa thức đặc trưng 16 1.3 Bán kính ổn định 21 1.4 Tính ổn định không phụ thuộc trễ 23 1.5 Ví dụ .25 Chương 2 Hệ rời rạc cấp cao 27 2.1 Tính ổn định của hệ dương và đa thức đặc trưng 28 2.2 Bán kính ổn định 31 2.3 Ví dụ 36 Chương 3 Phương trình sai phân 39 3.1 Tính ổn định của phương trình sai phân dương 40 3.2 Tính ổn định của hệ phương trình sai phân phụ thuộc tham số 45 3.3 Bán kính ổn định 47 3.3.1 Hệ sai phân phụ thuộc tham số 47 3.3.2 Phương trình sai phân 53 3.4 Ví dụ 55 Phần 2: Bán kính điều khiển được 57 Chương 4 Vô hạn chiều 58 4.1 Kiến thức cơ bản 59 4.2 Bán kính điều khiển được 63 4.2.1 Nhiễu trên cả A và B 63 4.2.2 Nhiễu trên chỉ A 64 4.2.3 Nhiễu trên chỉ B 65 4.2.4 Bán kính điều khiển được thực và phức 66 4.3 Ví dụ 68 Chương 5 Hữu hạn chiều 69 5.1 Kiến thức cơ bản 71 5.2 Bán kính điều khiển được có cấu trúc 74 5.2.1 Nhiễu trên cả A và B 74 5.2.2 Nhiễu trên chỉ A 77 5.2.3 Nhiễu trên chỉ B 79 5.3 Tính bán kính điều khiển được có cấu trúc 80 Chương 6 Thuật toán tính toán 83 6.1 Mở rộng kết quả của Gu 85 6.2 Thuật toán chia ba 87 6.2.1 Thực hiện kiểm tra Gu mở rộng 88 6.2.2 Tìm trị riêng 90 6.3 Kết quả thực nghiệm 91 6.4 Bán kính ổn định hóa được 92 Ket luận 97 Danh mục công trình 99 Tài liệu tham khảo 101

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