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  • 2022-06-07
    求下列差分方程所描述的[tex=1.714x1.0]ptAt65AfwA4koryK6UNdFg==[/tex]离散系统的零输入响应、零状态响应和全响应。[br][/br][tex=19.643x1.357]gVzaoqtwrme/yxT2qYwg7XoIuXQTskYR/d6k6A0QZrnBfW/OysIYnEBeH18P6YQH[/tex]
    •   先求零状态响应。系统的零状态响应满足 [tex=13.5x1.357]Tha6DT95a++UpC+RTAgrZCw4GlDgwgvyw3lrdvJL8q+tT1FEHBA4kgPkHDB1FsT8[/tex]令 [tex=1.929x1.0]rWpiA5mn2p7iuZx/oVniRw==[/tex], 得 [tex=16.857x1.357]n8z11RuXOSv786sDyfmtbng/YbOdlN+eHEHUogOA0Zeun429EstHLW155GW2mXJDWQ3bKhmvzPs8KZkTY25E1YMl6Pji2nJ5tmS55UVuJ+s=[/tex]令 [tex=1.929x1.0]iy49FZmj3Bn8sRaLZpfrEw==[/tex], 得 [tex=16.143x1.357]qTao6YdYhrFyL50WFYd+WEU+yhorX1n4HXwmBDBT+L6SuUB2vYrCG6YaGLpseJr7B36x8AERbvvRsqG8lc71Kd+prFfQse++hKnE5pQulu4=[/tex]系统的特征方程为[tex=4.929x1.357]dMDUzU4y3VDGrkhdS/lVlz2F0LjPp1ZBzLW7aGP4PKI=[/tex], 则特征根为 [tex=5.5x1.214]Mi4RogFSNEUtejDKNN7cItG50EXgq5YLQnetEHZRRRo=[/tex], [br][/br]方程的齐次解为[p=align:center][tex=10.857x1.357]v6AH35fqg/SXNLQ+0C+nhsTGQv7OVTBi6aGN9ZhgU/eXiKGPEWbbyyIBk88/9ooI[/tex]设其特解为[tex=4.429x1.357]Y2iZvm7+XKASg6B4MIKUj5P/socc/KQOhNZe+MIVA9U=[/tex], 代入零状态响应方程，解得[tex=2.5x2.357]1Mr7qKuLFwvWi4LRqv9W2g==[/tex], [br][/br]故特解为[p=align:center][tex=5.357x2.357]AIFd21JznMWICd9Eev1ChRnyCrDOFKePw80j9uFkSsc=[/tex]所以[p=align:center][tex=13.143x2.357]UdgS6A9Ad23M3BQ2B2D8z9xNLU29Fsvp9WVH63BMsk3PSRHP6UgWXz8DjqajFJpSL1MI9nF0HlaRZu6RRja8ig==[/tex][p=align:center][tex=12.429x5.214]fnpmC2J6JmQBLyo5NmGAz0YRV4PhtweoJrRjuJ/t4dVDEwCVjveUAnc/PfkFhC1UWO3e3PsqDYfVL4IAqIuI6QjJ6ek35GOzZmjDWJYyebOvK8wLg7ht0wQJ8AtivcEqI/d560Qm1RqizG2Ig1m0/VS/57cUE+ZmoLFIDyKFXq0=[/tex]      解得     [tex=4.643x5.214]fnpmC2J6JmQBLyo5NmGAz+ETO4TgGPJW4b16EanFO/8WOoLvyDugmsn4OPBSz7QbKob7RmKSFqB5OG9mg4zL2BEGK5OVTZ0jW9BZobcp9gpYdCR47j3900r/swkNJ0Z3[/tex]所以方程的零状态响应为[p=align:center][tex=15.214x2.786]H8Q6uVy9HrKuddoGeZoAHLSRwPoirY5WCfT0LXiENul/xU2lSBsft0SeLDoOPofBGI/AYw/UM4MwOTW5H2TYuY5xvW/fx8MUOuDgLynR9gwpe67TJ27CxVlDWF+0Xb/1[/tex][br][/br]零输入响应满足[p=align:center][tex=13.214x3.071]UD5Uh4Sf0JOreHxD3gt15qGQ94GLsEfxncPOoaKqoGGkBtgN7JZxCzT7h/uhEkYIsZUsdc/jJ3RM+70NhA02+aYz86WyUw0lOd1jPdRi98BFqO6YjXEjI1m5a9pT6CK6jAc2v751OSWpUWDueSecXODcGNgi4xEsi9+F8mPnCMQ=[/tex]代入初始值 [tex=12.0x3.357]7EJHVCtO2IWq3KpdB+jQsqrCoGhFW7SP6Icjg5nxBiPzTN8wJW6JG7ySjs/IPwkUHyvFJ3cEkRiz5YpqZqxE3NhUAVYVfbxWKElkSZIg0wJ8yQOEKuk1D1hB5hmTLq2gliSX3KbM8K9YG5SzYFjwjw==[/tex]得[tex=8.0x2.786]7EJHVCtO2IWq3KpdB+jQsrqF+y2Oi/LxJASD6vOfD9KqqBp4vccvowq6SEXNtn25yyYwcpU5T2i43B9rbvVT4RqKjXPVEEUSOp7OkDsWJAs=[/tex]解得 [tex=5.929x5.214]7EJHVCtO2IWq3KpdB+jQsvAT5AM4I9TxuT4wo1j+7dryrNJX6BtFZY8BtEwdqxbB+YZbn/Y4ZlBRTvlHorcNVIP0JmyHFQbyVSC+cqji+gHgMC+U8/J1S8zrp0xO0/FG[/tex]所以[p=align:center][tex=14.5x2.786]S5yGEyypDHJaiymDAd1V3iu/S+ClVJzPi31Qfh9OW80xHjgiGR/BQ9+dtcU0b28cJcBiX9qO5yBMFCnbGPvIQAmF1yM8+mhq8A5vumrKmjw=[/tex]离散系统的全响应为[p=align:center][tex=14.714x2.786]vOOzuHN4b95Nm8/G7r/dZd1a5T+XiMS8DLtkuKnZwwUmv6vmM+7rqO+a5NqL6Q73sY+Bxc+uD5IrWmjv59zWMvuHi0f9bTYIJWPFT9GXwXA=[/tex]
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    • 0

      求下列差分方程所描述的[tex=1.714x1.0]ptAt65AfwA4koryK6UNdFg==[/tex]离散系统的零输入响应。[br][/br][tex=20.571x1.357]IyzBadgxP2Sp12LeFgykYNwwjHm+ktSPvxSUWvxQ3BpCB0WJLkFS4yQ7ah4pJfhF[/tex]

    • 1

      求下列差分方程所描述的[tex=1.714x1.0]ptAt65AfwA4koryK6UNdFg==[/tex]离散系统的零输入响应。[tex=25.714x1.357]qVXezHvNospgVmjfnuVtdkoNIbqi4CllTxHI9DozNCnEz83H7AVTkYSuU4f+bf2zuoY+xHHTauMwgPuzYlbz6Q==[/tex]

    • 2

      求下列差分方程所描述的[tex=1.714x1.0]ptAt65AfwA4koryK6UNdFg==[/tex]离散系统的零输入响应。[tex=20.143x1.357]bJkMxaGTAozxxicrfJhbCsnNxKBFEP3wkPRWBerB0QBtuLiR8kED2B6C3l7s93Cz[/tex]

    • 3

      求下列差分方程所描述的[tex=1.714x1.0]ptAt65AfwA4koryK6UNdFg==[/tex]离散系统的零输入响应。[tex=21.429x1.357]JAjWX54fdFVmqRUiQkE1HVCaY3aREk0JZp5r5uFDDqlVoD7gOX7MZ8/GYEEqGmt5jiMTC4VNjgGtC+bFTdch1g==[/tex]

    • 4

      求下列差分方程所描述的离散系统的零输入响应,零状态响应和全响应。[tex=19.071x1.357]zVtlD8wh3ZsJinYEiFPSrYwjUZ7xZeznNDrVSuJmROhzc3BkHp3P261cvCwaMSa7wpaunPBjOAt3+NTvesi3mw==[/tex]